Teaching

TEACHING DURING THE ACADEMIC YEAR 2025/2026

During the 2025-2026 academic year, I am revising and preparing the teaching material for the econometrics modules below, from a research and teaching focused perspective.

Econometric Methods I (Fall 2025)

Course Contents

Linear Regression Models (Large sample theory and hypothesis testing).

Estimation Methods for Linear Models (e.g., MLE, GMM, Two-Step Estimators) / Bootstrap Methods.

Time Series Econometrics (Unit Roots, Cointegration and Structural Breaks).

Simultaneous Equations Models and Panel Data Econometrics.

Further Topics: DiD, ATEs, Extremum Estimation and Quantile Regression Models.

# research-led teaching, # econometric theory and methods, # time series econometrics, # macroeconometrics, # applied econometrics, # machine learning methods

>> I am academic economist with a specialisation in econometrics.

>> I am an econometrician working on topics in time series econometrics, panel data econometrics and macroeconometrics.

Econometric Methods I (Fall 2025)

[Module under development: 7.5 ECTS]

Instructor: Dr. Christis Katsouris, Ph.D.

Lectures:

Office hours:

Email: christiskatsouris@gmail.com

Course Description

The course covers Econometric Theory and Methods.

Topics that are typically covered in an Econometric Methods I course include: Linear Regression Model (Large Sample Theory and Hypothesis Testing); Single-Equation and Multiple Equation GMM, IV, and MLE methods; Simultaneous Equation Models; Panel Data Models; Unit Root, Cointegration and Structural Breaks (single-equation vs multiple-equations); Extremum Estimation; Quantile Regression Models; DiD and Average Treatment Effects Estimation Methods.

Topics that are typically covered in an Econometric Methods II course include: Reduced Rank Regression; Nonlinear GMM; Nonlinear Panel Models; Nonparametric Regression/Series Regression; Binary and Multiple Choice; Censoring and Selection; Nonlinear Time Series Models; Machine Learning and Causal Inference Methods.

Course Contents

1). Linear Regression and IV Regression Models (Asymptotic theory, estimation, and hypothesis testing)

Single-Equation

Chapters: Hansen (Chapter 4, 5); Davidson & MacKinnon (Chapter 2, 3); Wooldridge (Chapter 5, 6); Hayeshi (Chapter 2, 3).
Articles: Goldsmith-Pinkham, Hull & Kolesár (2024, AER); Lee, McCrary, Moreira & Porter (2022, AER); Mills, Moreira & Vilela (2014, JoE).

Multiple-Equations

Chapters: Hansen (Chapter 12, 13); Davidson & MacKinnon (Chapter 8, 9); Wooldridge (Chapter 7, 8); Hayeshi (Chapter 4).
Articles: Bekker & Crudu (2015, JoE);

2). Unit Roots, Cointegration and Structural Breaks (Asymptotic theory, estimation, and hypothesis testing)

Single-Equation

Chapters: Hansen (Chapter 14, 16.1-16.15); Davidson & MacKinnon (Chapter 13.1-13.5, 14.1-14.5); Hayeshi (Chapter 9).
Articles: Phillips, P.C.B. (1987, Ecta);

Multiple-Equations

Chapters: Hansen (Chapter 15, 16.20-16.21); Davidson & MacKinnon (Chapter 13.7); Hayeshi (Chapter 10).
Articles: Phillips, P.C.B. & Hansen, B. (1990, RES); Johansen (1995, JoE); Bai, Lumsdaine & Stock (1998, RES);

3). Panel Data Regressions and Estimation Methods

Chapters: Hansen (Chapter 17); Wooldridge (Chapter 9, 10); Hayeshi (Chapter 5).
Articles: Stock & Watson (2008, Ecta); Fernández-Val & Vella (2011, JoE); Galvao & Kato (2014, JBES);

4). DiD and Average/Marginal TEs Estimation Methods

Chapters: Hansen (Chapter 18); Wooldridge (Chapter 18).
Articles: Abrevaya, Hsu & Lieli (2015, JBES);

5). Extremum Estimators and Quantile Regressions / Model Selection

Chapters: Hansen (Chapter 24); Wooldridge (Chapter 12); Hayeshi (Chapter 7); Hansen (Chapter 28).
Articles: Angrist, Chernozhukov & Fernández‐Val (2006, Ecta); Firpo, Fortin & Lemieux (2009, Ecta);

Lecture Notes

Lecture Slides will be provided.

Recommended Reading List

The course is designed to deliver both a theoretical econometric component and an applied econometric component with applications in economic and financial time series analysis. During lectures we will cover the econometric methods for estimation and inference with spatial panel data models. During the computer labs we will solve the workshop exercises using R/Stata packages, with a focus on applying the econometric methods covered in the course to panel datasets.

The reading list below includes supporting material and additional readings for the topics covered in class. Also main and additional textbooks are displayed below.

References

A. Literature on Spatial Econometrics:

Liu, X., and Prucha, I. R. (2025). "On Testing for Spatial or Social Network Dependence in Panel Data allowing for Network Variability". Journal of Econometrics, 247, 105925.
Okui, R., Sun, Y., and Wang, W. (2025). "Recovering Latent Linkage Structures and Spillover Effects with Structural Breaks in Panel Data Models". Preprint arXiv:2501.09517. [Macro Time Series Data]
Wang, L., and Li, K. (2025). "Spatial Panel Data Models with Structural Change". Journal of Econometrics, 251, 106078. [Macro Time Series Data]
Reuvers, H., and Wijler, E. (2024). "Sparse Generalized Yule–Walker Estimation for Large Spatio-Temporal Autoregressions with an Application to NO2 Satellite Data". Journal of Econometrics, 239(1), 105520.
Liang, X., Gao, J., and Gong, X. (2022). "Semiparametric Spatial Autoregressive Panel Data Model with Fixed Effects and Time-Varying Coefficients". Journal of Business & Economic Statistics, 40(4), 1784-1802. [Macro Time Series Data]
Yang, K., and Lee, L. F. (2021). "Estimation of Dynamic Panel Spatial Vector Autoregression: Stability and Spatial Multivariate Cointegration". Journal of Econometrics, 221(2), 337-367. [Macro/Trade Time Series Data]
Kuersteiner, G. M., and Prucha, I. R. (2020). "Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity". Econometrica, 88(5), 2109-2146.
Liu, L., Moon, H. R., and Schorfheide, F. (2020). "Forecasting with Dynamic Panel Data Models". Econometrica, 88(1), 171-201. [Financial/Banking Time Series Data]
Shen, S., and Pang, J. (2018). "Measuring the Diffusion of Housing Prices Across Space and Over Time: Replication and Further Evidence". Journal of Applied Econometrics, 33(3), 479-484.
Zhang, X., and Yu, J. (2018). "Spatial Weights Matrix Selection and Model Averaging for Spatial Autoregressive Models". Journal of Econometrics, 203(1), 1-18. [Macro Time Series Data]
Li, K. (2017). "Fixed-Effects Dynamic Spatial Panel Data Models and Impulse Response Analysis". Journal of Econometrics, 198(1), 102-121.
Su, L., and Qu, X. (2017). "Specification Test for Spatial Autoregressive Models". Journal of Business & Economic Statistics, 35(4), 572-584. [Macro Time Series Data]
Shi, W., and Lee, L. F. (2017). "Spatial Dynamic Panel Data Models with Interactive Fixed Effects". Journal of Econometrics, 197(2), 323-347. [Macro Time Series Data]
Qu, X., Lee, L. F., and Yu, J. (2017). "QML Estimation of Spatial Dynamic Panel Data Models with Endogenous Time Varying Spatial Weights Matrices". Journal of Econometrics, 197(2), 173-201. [Price Data]
Blasques, F., Koopman, S. J., Lucas, A., and Schaumburg, J. (2016). "Spillover Dynamics for Systemic Risk Measurement using Spatial Financial Time Series Models". Journal of Econometrics, 195(2), 211-223. [Financial Time Series Data]
Lee, L. F., and Yu, J. (2014). "Efficient GMM Estimation of Spatial Dynamic Panel Data Models with Fixed Effects". Journal of Econometrics, 180(2), 174-197. [Macro Time Series Data]
Brady, R. R. (2011). "Measuring the Diffusion of Housing Prices Across Space and Over Time". Journal of Applied Econometrics, 26(2), 213-231.

B. Literature on Spatial Time Series Analysis:

Tobar, A., et al. (2025). "Spatial Disaggregation of Time Series". Preprint arXiv:2509.04065.
Schennach, S. M., and Starck, V. (2025). "Using Spatial Modelling to Address Covariate Measurement Error". Preprint arXiv:2511.03306.
Müller, U. K., and Watson, M. W. (2024). "Spatial Unit Roots and Spurious Regression". Econometrica, 92(5), 1661-1695.
Müller, U. K., and Watson, M. W. (2023). "Spatial Correlation Robust Inference in Linear Regression and Panel Models". Journal of Business & Economic Statistics, 41(4), 1050-1064.
Müller, U. K., and Watson, M. W. (2022). "Spatial Correlation Robust Inference". Econometrica, 90(6), 2901-2935.

C. Literature on Local Economic Growth and Business Cycles:

Peters, M., and Walsh, C. (2026). "Population Growth and Firm Dynamics". Journal of Political Economy Macroeconomics (forthcoming).
Berkes, E., Gaetani, R., and Mestieri, M. (2025). "Technological Waves, Knowledge Diffusion, and Local Growth". Journal of Political Economy Macroeconomics, 3(1), 75-121.
Drechsel-Grau, M., and Greimel, F. (2025). "Falling Behind: Has Rising Inequality Fueled the American Debt Boom?". Review of Financial Studies, hhaf062.
Adão, R., Beraja, M., and Pandalai-Nayar, N. (2024). "Fast and Slow Technological Transitions". Journal of Political Economy Macroeconomics, 2(2), 183-227.
Couture, V., Gaubert, C., Handbury, J., and Hurst, E. (2024). "Income Growth and the Distributional Effects of Urban Spatial Sorting". Review of Economic Studies, 91(2), 858-898.
Giroud, X., Lenzu, S., Maingi, Q., and Mueller, H. (2024). "Propagation and Amplification of Local Productivity Spillovers". Econometrica, 92(5), 1589-1619.
Bilal, A. (2023). "The Geography of Unemployment". Quarterly Journal of Economics, 138(3), 1507-1576.
Cai, J., Li, N., and Santacreu, A. M. (2022). "Knowledge Diffusion, Trade, and Innovation across Countries and Sectors". American Economic Journal: Macroeconomics, 14(1), 104-145.
Vom Lehn, C., and Winberry, T. (2022). "The Investment Network, Sectoral Comovement, and the Changing US Business Cycle". Quarterly Journal of Economics, 137(1), 387-433.
Bilal, A., and Rossi‐Hansberg, E. (2021). "Location as an Asset". Econometrica, 89(5), 2459-2495.
Fajgelbaum, P. D., and Gaubert, C. (2020). "Optimal Spatial Policies, Geography, and Sorting". Quarterly Journal of Economics, 135(2), 959-1036.
Beraja, M., Fuster, A., Hurst, E., and Vavra, J. (2019). "Regional Heterogeneity and the Refinancing Channel of Monetary Policy". Quarterly Journal of Economics, 134(1), 109-183.
Beraja, M., Hurst, E., and Ospina, J. (2019). "The Aggregate Implications of Regional Business Cycles". Econometrica, 87(6), 1789-1833.
Giroud, X., and Mueller, H. M. (2018). "Firm Leverage and Regional Business Cycles". NBER Working Paper (No. w25325). Available at nber/w25325.
Schennach, S. M. (2018). "Long Memory via Networking". Econometrica, 86(6), 2221-2248.

Bibliography

Textbooks

Hansen, B. (2022). Econometrics. Princeton University Press (1st Edition).
Hsiao, C. (2022). Analysis of Panel Data. Cambridge University Press (4th Edition).
Baltagi, B. H. (2021). Econometric Analysis of Panel Data. Springer (6th Edition).
Martin, V., Hurn, S., and Harris, D. (2013). Econometric Modelling with Time Series: Specification, Estimation and Testing. Cambridge University Press (1st Edition).
Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data. MIT Press (2nd Edition).
LeSage, J., and Pace, R. K. (2009). Introduction to Spatial Econometrics. Chapman and Hall/CRC.

Statistical Software

Heiss, F. (2020). Using R for Introductory Econometrics. Germany: Florian Heiss (2nd Edition).
Croissant, Y., and Millo, G. (2019). Panel Data Econometrics with R. John Wiley & Sons.

TEACHING DURING THE ACADEMIC YEAR 2024/2025

During the 2024-2025 academic year, I am revising and preparing the teaching material for the econometrics modules below.

Econometrics

(Undergraduate: 7.5 ECTS or 15 Credits).

Lecture Notes in Econometrics

Applied Macroeconometrics II

(Graduate: 7.5 ECTS or 15 Credits).

Lecture Notes in Macroeconometrics

Photo Credit: © Christis Katsouris (2019)

Applied Macroeconometrics II

Last updated: March 14, 2025

Module Description:

The module Applied Macroeconometrics II aims to cover methodological and empirical issues related to the implementation of SVAR and DSGE models. Emphasis will be given to deeper the understanding of identification issues of the Structural VAR model such as identification by sign restrictions and additional identification schemes for DSGE models (partial versus full identification). We consider theoretical time series properties (invertability versus non-invertability) which are relevant to identification validity. We focus on the estimation methodologies and specification analysis issues including model validation and model adequacy techniques as well as statistical robustness procedures to model misspecification. Moreover, the bayesian approach to SVAR and DSGE modelling will be covered. Empirical applications for the econometric methods covered throughout the module will be emphasized through article presentations and software illustrations (R/Matlab) using macroeconomic data.

The course is suitable for MRes/PhD students in Economics (Year 2 of MRes in Economics). Prerequisite modules: Econometrics and Macroeconomics at the postgraduate level. As an Advanced Econometrics module we discuss identification schemes, estimation and hypothesis testing, model validation and/or specification analysis as well as empirical applications which are relevant to policy-making (policy shocks versus non-policy shocks). Specifically, policy-relevant shocks include monetary and fiscal policy shocks (unexpected movements), while non-policy shocks include oil price shocks, energy price shocks, technology shocks, financial shocks as well as uncertainty shocks. In particular, uncertainty shocks include economic policy uncertainty shocks as well as climate policy uncertainty shocks. We discuss related case studies from the literature as illustrative examples. To facilitate participation during lectures, some preparation before classes is essential and recommended.

We give emphasis on appropriate quantitative methods and on strategies regarding how to address commonly encountered problems for the identification of SVAR and DSGE models. For example, the data missingness problem, poses a credibility-efficiency trade-off that can be solved by viewing the narrative identification approach as a missing data problem. We discuss procedures from Bayesian statistics which permit robust estimation and inference regardless of the features in the data at hand. Building on the theory of observationally equivalent processes, we consider that model parameters obtained from such equivalent representations, permit the construction of impulse response functions as a joint conditional distribution function estimation step. Moreover, we discuss the notion of bayesian asymptotically valid inference, which can be conducted by constructing the variance using the sandwich formula of Chernozhukov and Hong (2003) (see, Guerron-Quintana, P., Inoue, A., and Kilian, L. (2017, JoE)).

Related model selection problems associated with SVAR and DSGE models involve the choice of the family of prior distributions which best describes our prior beliefs about the state of the economy. In other words, the bayesian analysis for SVAR and DSGE models requires to careful consider the choice of prior distributions. Specifically, when conducting bayesian inference with SVAR models, the specification of the prior distributions for the unknown parameters of the model can affect the accuracy of estimated results. From the computational perspective, we use suitable prior distributions for the parameters of the SVAR model (such as the Minnesota prior and the normal-inverse-Wishart prior; usually preference is given to priors with closed-form solutions), which can ensure uniform conditional inferences (such as estimates and statistics are obtained conditional on the reduced-form parameters). Bayesian model selection techniques for SVAR and DSGE models can then be applied as well as diagnostic tools. In particular, implementing statistical model adequacy procedures allows to evaluate the sensitivity of DSGE models which are estimated via algorithmic procedures (such as the MCMC algorithm). Moreover, the predictive ability of these procedures can be assessed using predictive performance measures with respect to changes in the prior distribution. Conducting sensitivity analysis for empirical findings to the choice of identifying assumptions is a crucial component of econometric and specification analysis.

Research Project:

Regarding the main assignment for the course, Part I & II include topics suitable to examine in the research project. For example, a monte carlo study to compare finite-sample performance of impulse response functions via different estimation methods. Another example, is to study the joint bayesian inference procedures of DSGE models using VAR representations. Overall, aspects of unified bayesian-frequentist inference for SVAR models is an open domain with many possible applications especially with respect to uncertainty quantification comparisons.

Module Syllabus:

Part I. Bayesian and Classical Identification of SVAR & DSGE Models

Identification of SVAR Models

Funovits, B. (2024). "Identifiability and Estimation of Possibly Non-invertible SVARMA Models: The Normalised Canonical WHF Parametrisation". Journal of Econometrics, 241(2), 105766.
Lütkepohl, H., Shang, F., Uzeda, L., and Woźniak, T. (2024). "Partial Identification of Heteroskedastic Structural VARs: Theory and Bayesian Inference". Preprint arXiv:2404.11057.
Anttonen, J., Lanne, M., and Luoto, J. (2023). "Bayesian Inference on Fully and Partially Identified Structural Vector Autoregressions". Available at SSRN 4358059.
Braun, R. (2023). "The Importance of Supply and Demand for Oil Prices: Evidence from Non‐Gaussianity". Quantitative Economics, 14(4), 1163-1198.
Lanne, M., and Luoto, J. (2020). "Identification of Economic Shocks by Inequality Constraints in Bayesian Structural Vector Autoregression". Oxford Bulletin of Economics and Statistics, 82(2), 425-452.
Granziera, E., Moon, H.R., and Schorfheide, F. (2018). "Inference for VARs Identified with Sign Restrictions". Quantitative Economics, 9(3), 1087-1121.
Baumeister, C., and Hamilton, J.D. (2015). "Sign Restrictions, Structural Vector Autoregressions, and useful Prior Information". Econometrica, 83(5), 1963-1999.

Identification of DSGE Models

Kocięcki, A., and Kolasa, M. (2023). "A Solution to the Global Identification Problem in DSGE Models". Journal of Econometrics, 236(2), 105477.
Drautzburg, T. (2020). "A Narrative Approach to a Fiscal DSGE Model". Quantitative Economics, 11(2), 801-837.
Lanne, M., and Luoto, J. (2018). "Data‐Driven Identification Constraints for DSGE Models". Oxford Bulletin of Economics and Statistics, 80(2), 236-258.
Kocięcki, A., and Kolasa, M. (2018). "Global Identification of Linearized DSGE Models". Quantitative Economics, 9(3), 1243-1263.
Qu, Z., and Tkachenko, D. (2017). "Global Identification in DSGE Models allowing for Indeterminacy". Review of Economic Studies, 84(3), 1306-1345.
Giacomini, R. (2013). "The Relationship between DSGE and VAR Models". Advances in Econometrics, 32, 1-25.
Guerron‐Quintana, P., Inoue, A., and Kilian, L. (2013). "Frequentist Inference in Weakly Identified Dynamic Stochastic General Equilibrium Models". Quantitative Economics, 4(2), 197-229.
Koop, G., Pesaran, M.H., and Smith, R.P. (2013). "On Identification of Bayesian DSGE Models". Journal of Business & Economic Statistics, 31(3), 300-314.
Brzoza-Brzezina, M., Kolasa, M., and Makarski, K. (2013). "The Anatomy of Standard DSGE Models with Financial Frictions". Journal of Economic Dynamics and Control, 37(1), 32-51.
Qu, Z., and Tkachenko, D. (2012). "Identification and Frequency Domain Quasi‐Maximum Likelihood Estimation of Linearized DSGE Models". Quantitative Economics, 3(1), 95-132.
Iskrev, N. (2010). "Local Identification in DSGE Models". Journal of Monetary Economics, 57(2), 189-202.
Consolo, A., Favero, C.A., and Paccagnini, A. (2009). "On the Statistical Identification of DSGE Models". Journal of Econometrics, 150(1), 99-115.
Ravenna, F. (2007). "Vector Autoregressions and Reduced form Representations of DSGE Models". Journal of Monetary Economics, 54(7), 2048-2064.

Identification of New Keynesian Phillips Curve (NKPC) Models

Barnichon, R., and Mesters, G. (2024). "Improving the Power-Credibility Trade-off in Macroeconomic Models". Working paper, University Pompeu Fabra.
Lewis, D.J., and Mertens, K. (2022). "Dynamic Identification Using System Projections and Instrumental Variables". CEPR Discussion Paper No. DP17153. Available at SSRN 4121257.
Barnichon, R., and Mesters, G. (2020). "Identifying Modern Macro Equations with Old Shocks". Quarterly Journal of Economics, 135(4), 2255-2298.
Fanelli, L. (2012). "Determinacy, Indeterminacy and Dynamic Misspecification in Linear Rational Expectations Models". Journal of Econometrics, 170(1), 153-163.
Komunjer, I., and Ng, S. (2011). "Dynamic Identification of Dynamic Stochastic General Equilibrium Models". Econometrica, 79(6), 1995-2032.

Time-Varying Identification of SVAR Models

Camehl, A., and Woźniak, T. (2025). "Time-Varying Identification of Structural Vector Autoregressions". Preprint arxiv:2502.19659.
Lütkepohl, H., and Strohsal, T. (2025). "Time-Varying Shock Transmission in Non-Gaussian Structural Vector Autoregressions". German Institute for Economic Research Working paper (No. 2110). Available at DIW Berlin.

Part II. Bayesian and Classical Analysis of SVAR & DSGE Models

Bayesian Local Projections

Huber, F., Matthes, C., and Pfarrhofer, M. (2024). "General Seemingly Unrelated Local Projections". Preprint arXiv:2410.17105.
Ferreira, L.N., Miranda-Agrippino, S., and Ricco, G. (2023). "Bayesian Local Projections". Review of Economics and Statistics, 1-45.

Prior Selection and Impulse Responses

Kilian, L. (2025). "Impulse Response Diagnostics for Priors on Parameters in Structural Vector Autoregressions". FRB of Dallas Working Paper (No. 2507). Available at SSRN 5158202.
Wiesen, T. F., and Beaumont, P. M. (2024). "A Joint Impulse Response Function for Vector Autoregressive Models". Empirical Economics, 66(4), 1553-1585.
Arias, J., Rubio-Ramirez, J.F., and Waggoner, D.F. (2023). "Uniform Priors for Impulse Responses". FRB of Atlanta Working Paper (No. 2023-13). Available at SSRN 4587403.
Inoue, A., and Kilian, L. (2022). "Joint Bayesian Inference about Impulse Responses in VAR Models". Journal of Econometrics, 231(2), 457-476.
Inoue, A., and Kilian, L. (2021). "The Role of the Prior in Estimating VAR Models with Sign Restrictions". Center for Financial Studies Working Paper, (660). Available at SSRN 3963314.
Lütkepohl, H., Staszewska-Bystrova, A., and Winker, P. (2020). "Constructing Joint Confidence Bands for Impulse Response Functions of VAR Models". Econometrics and Statistics, 13, 69-83.
Plagborg‐Møller, M. (2019). "Bayesian Inference on Structural Impulse Response Functions". Quantitative Economics, 10(1), 145-184.
Montiel Olea, J. L., and Plagborg‐Møller, M. (2019). "Simultaneous Confidence Bands: Theory, Implementation, and an Application to SVARs". Journal of Applied Econometrics, 34(1), 1-17.
Bruder, S., and Wolf, M. (2018). "Balanced Bootstrap Joint Confidence Bands for Structural Impulse Response Functions". Journal of Time Series Analysis, 39(5), 641-664.
Guerron-Quintana, P., Inoue, A., and Kilian, L. (2017). "Impulse Response Matching Estimators for DSGE Models". Journal of Econometrics, 196(1), 144-155.
Inoue, A., and Kilian, L. (2016). "Joint Confidence Sets for Structural Impulse Responses". Journal of Econometrics, 192(2), 421-432.
Giannone, D., Lenza, M., and Primiceri, G.E. (2015). "Prior Selection for Vector Autoregressions". Review of Economics and Statistics, 97(2), 436-451.
Lütkepohl, H., Staszewska‐Bystrova, A., and Winker, P. (2015). "Confidence Bands for Impulse Responses: Bonferroni vs. Wald". Oxford Bulletin of Economics and Statistics, 77(6), 800-821.
Inoue, A., and Kilian, L. (2013). "Inference on Impulse Response Functions in Structural VAR Models". Journal of Econometrics, 177(1), 1-13.
Kocięcki, A. (2010). "A Prior for Impulse Responses in Bayesian Structural VAR Models". Journal of Business & Economic Statistics, 28(1), 115-127.
Jordà, Ò. (2009). "Simultaneous Confidence Regions for Impulse Responses". Review of Economics and Statistics, 91(3), 629-647.
Del Negro, M., and Schorfheide, F. (2008). "Forming Priors for DSGE Models (and how it affects the assessment of nominal rigidities)". Journal of Monetary Economics, 55(7), 1191-1208.

Bayesian Inference for Set-Identified SVARs

Bacchiocchi, E., Bastianin, A., Kitagawa, T., and Mirto, E. (2024). "Partially Identified Heteroskedastic SVARs". Preprint arXiv:2403.06879.
Nguyen, L. (2024). "Bayesian Inference in Structural Vector Autoregression with Sign Restrictions and External Instruments". Available at SSRN 4680099.
Armstrong, T.B., Kolesár, M., and Plagborg‐Møller, M. (2022). "Robust Empirical Bayes Confidence Intervals". Econometrica, 90(6), 2567-2602.
Giacomini, R., Kitagawa, T., and Read, M. (2022). "Robust Bayesian Inference in Proxy SVARs". Journal of Econometrics, 228(1), 107-126.
Giacomini, R., and Kitagawa, T. (2021). "Robust Bayesian Inference for Set‐Identified Models". Econometrica, 89(4), 1519-1556.
Caldara, D., and Herbst, E. (2019). "Monetary Policy, Real Activity, and Credit Spreads: Evidence from Bayesian Proxy SVARs". American Economic Journal: Macroeconomics, 11(1), 157-192.
Gafarov, B., Meier, M., and Olea, J.L.M. (2018). "Delta-Method Inference for a Class of Set-Identified SVARs". Journal of Econometrics, 203(2), 316-327.

Bayesian Inference for Exactly-Identified SVARs

Gutiérrez, I., Alvares, D., and Gutiérrez, L. (2024). "A Bayesian Flexible Model for Testing Granger Causality". Econometrics and Statistics.
Liu, X., Li, Y., Yu, J., and Zeng, T. (2022). "Posterior-based Wald-type Statistics for Hypothesis Testing". Journal of Econometrics, 230(1), 83-113.
Komunjer, I., and Zhu, Y. (2020). "Likelihood Ratio Testing in Linear State Space Models: An Application to Dynamic Stochastic General Equilibrium Models". Journal of Econometrics, 218(2), 561-586.

Bayesian Analysis of DSGE Models

Benigno, G., Foerster, A., Otrok, C., and Rebucci, A. (2025). "Estimating Macroeconomic Models of Financial Crises: An Endogenous Regime‐Switching Approach". Quantitative Economics, 16(1), 1-47.
Petrova, K. (2024). "On the Validity of Classical and Bayesian DSGE-Based Inference". FRB of New York Staff Report (No. 1084). Available at SSRN 4698481.
Filippeli, T., Harrison, R., and Theodoridis, K. (2020). "DSGE-based Priors for BVARs and Quasi-Bayesian DSGE Estimation". Econometrics and Statistics, 16, 1-27.
Chin, K. H., and Li, X. (2019). "Bayesian Forecast Combination in VAR-DSGE Models". Journal of Macroeconomics, 59, 278-298.
Hirose, Y., and Naganuma, S. (2010). "Structural Estimation of the Output Gap: A Bayesian DSGE Approach". Economic Inquiry, 48(4), 864-879.
An, S., and Schorfheide, F. (2007). "Bayesian Analysis of DSGE Models". Econometric Reviews, 26(2-4), 113-172.
Bierens, H.J. (2007). "Econometric Analysis of Linearized Singular Dynamic Stochastic General Equilibrium Models". Journal of Econometrics, 136(2), 595-627.

Part III. Bayesian Estimation and Model Validation of SVAR & DSGE Models

Model Selection & Bayesian Inference under Misspecification

Bacchiocchi, E., and Kitagawa, T. (2024). "SVARs with Breaks: Identification and Inference". Preprint arXiv:2405.04973.
Frazier, D.T., Kohn, R., Drovandi, C., and Gunawan, D. (2023). "Reliable Bayesian Inference in Misspecified Models". Preprint arXiv:2302.06031.
Shimizu, K. (2023). "Asymptotic Properties of Bayesian Inference in Linear Regression with a Structural Break". Journal of Econometrics, 235(1), 202-219.
Petrova, K. (2022). "Asymptotically Valid Bayesian Inference in the presence of Distributional Misspecification in VAR Models". Journal of Econometrics, 230(1), 154-182.
Inoue, A., Kuo, C.H., and Rossi, B. (2020). "Identifying the Sources of Model Misspecification". Journal of Monetary Economics, 110, 1-18.
Hsu, H.L., Ing, C.K., and Tong, H. (2019). "On Model Selection from a Finite Family of Possibly Misspecified Time Series Models". Annals of Statistics, 47(2), 1061-1087.
Inoue, A., and Shintani, M. (2018). "Quasi‐Bayesian Model Selection". Quantitative Economics, 9(3), 1265-1297.
Müller, U.K. (2013). "Risk of Bayesian Inference in Misspecified Models, and the Sandwich Covariance Matrix". Econometrica, 81(5), 1805-1849.
Walker, S.G. (2013). "Bayesian Inference with Misspecified Models". Journal of Statistical Planning and Inference, 143(10), 1621-1633.
Waggoner, D. F., and Zha, T. (2012). "Confronting Model Misspecification in Macroeconomics". Journal of Econometrics, 171(2), 167-184.

Remark 1.

The concept of model misspecification commonly discussed within the econometrics, macroeconometrics and statistics literature, is not an argument regarding which model best fits the underline data generating process, such as whether fitting a VAR(1) model versus fitting a VAR(p) model provides a closer representation to the true model. In fact, the stability conditions of a macroeconomic system is based on the general VAR(p) setting along with the related conditions on the roots of the characteristic equation (order selection can be of course implemented at the modelling stage). Thus, model misspecification refers to both the identification problem in econometrics and in practice whether any misspecifiction on the distributional assumptions may affect parameter identification and thus estimation of functionals of model parameters (such as the impulse response functions). From the bayesian perspective, the presence of possible model misspecification is related to the problem of poor uncertainty quantification, which can impact the construction of confidence bands, the consistent estimation of posterior density functions and predictive intervals. For example, Chernozhukov and Hong (2003, JoE) developed general results for asymptotic posterior consistency, normality and coverage of confidence/credible intervals based on Gibbs posteriors. Overall, available parameter estimation and approximation techniques are based on linear and non-linear filters, MCMC algorithms and the variational inference approach.

In general, we are interested to identify the sources of model misspecification (such as due to issues of indeterminacy and weak identification). From the classical estimation perspective, a DSGE modelling framework, permits the construction of frequency-domain driven statistics for testing the null of correct model specification, based on the divergence between the log-likelihood and its expected value under the data generating process. From the bayesian perspective, assessing the correct distributional assumptions can be done using asymptotically valid bayesian inference arguments under the presence of possible misspecification. However, recently it has been shown that parameter estimators which heavily rely on moment restrictions, such as the GMM, are inadmissable under the presence of weak identification (see, Andrews & Mikusheva (2022, Preprint arXiv:2204.12462)). Overall, model checking and misspecification testing is indeed a crucial component of the econometric analysis. Econometric inference for model misspecification involves considering statistical deviations from the true model in order to establish asymptotically valid inference. We also consider the variable selection problem separately from the model misspecification problem to deepen our understanding of the key underpinnings for each setting.

Offline and Online Estimation of SVAR & DSGE Models

Braun, R., Kapetanios, G., and Marcellino, M.G. (2025). "Nonparametric Time Varying IV-SVARs: Estimation and Inference". FEDS Working Paper (No. 2025-004). Available at SSRN 5094784.
Arias, J., Rubio-Ramirez, J.F., Shin, M., and Waggoner, D.F. (2024). "Inference based on Time-Varying SVARs Identified with Sign Restrictions". FRB of Philadelphia Working Paper (No. 24-18). Available at SSRN 5037156.
Cai, M., et al. (2021). "Online Estimation of DSGE Models". The Econometrics Journal, 24(1), C33-C58.
Petrova, K. (2019). "A Quasi-Bayesian Local Likelihood Approach to Time Varying Parameter VAR Models". Journal of Econometrics, 212(1), 286-306.
Diebold, F.X., Schorfheide, F., and Shin, M. (2017). "Real-Time Forecast Evaluation of DSGE Models with Stochastic Volatility". Journal of Econometrics, 201(2), 322-332.
Gorodnichenko, Y., and Ng, S. (2010). "Estimation of DSGE Models when the Data are Persistent". Journal of Monetary Economics, 57(3), 325-340.

Part IV. Large Bayesian Model Representations

Estimation & Inference for Large Bayesian Models

Chan, J. C., and Pfarrhofer, M. (2025). "Large Bayesian VARs for Binary and Censored Variables". Preprint arXiv:2506.01422.
Davidson, S. N., Hou, C., and Koop, G. (2025). "Investigating Economic Uncertainty using Stochastic Volatility in Mean VARs: The Importance of Model Size, Order-Invariance and Classification". Journal of Business & Economic Statistics, 1-16.
Bernardi, M., Bianchi, D., and Bianco, N. (2024). "Variational Inference for Large Bayesian Vector Autoregressions". Journal of Business & Economic Statistics, 1-17.
Chan, J. C., Koop, G., and Yu, X. (2024). "Large Order-Invariant Bayesian VARs with Stochastic Volatility". Journal of Business & Economic Statistics, 42(2), 825-837.
Hou, C. (2024). "Large Bayesian SVARs with Linear Restrictions". Journal of Econometrics, 244(1), 105850.
Chan, J. C., Poon, A., and Zhu, D. (2023). "High-Dimensional Conditionally Gaussian State Space Models with Missing Data". Journal of Econometrics, 236(1), 105468.
Cross, J. L., Hou, C., Koop, G., and Poon, A. (2023). "Large Stochastic Volatility in Mean VARs". Journal of Econometrics, 236(1), 105469.
Lippi, M. (2023). "Validating DSGE Models with SVARs and High-Dimensional Dynamic Factor Models". Econometric Theory, 39(6), 1273-1291.
Ray, K., and Szabó, B. (2022). "Variational Bayes for High-Dimensional Linear Regression with Sparse Priors". Journal of the American Statistical Association, 117(539), 1270-1281.
Chan, J.C. (2022). "Asymmetric Conjugate Priors for Large Bayesian VARs". Quantitative Economics, 13(3), 1145-1169.
Chan, J. C., Eisenstat, E., and Koop, G. (2016). "Large Bayesian VARMAs". Journal of Econometrics, 192(2), 374-390.
Morris, S.D. (2016). "VARMA Representation of DSGE Models". Economics Letters, 138, 30-33.
Chan, J. C., and Strachan, R.W. (2012). "Estimation in Non-Linear Non-Gaussian State Space Models with Precision-based Methods". Available at SSRN 2025754.

Estimation for Time-Varying Bayesian Models

He, Z. (2024). "Time-Dependent Shrinkage of Time-Varying Parameter Regression Models". Econometric Reviews, 43(1), 1-29.
Huber, F., Koop, G., and Onorante, L. (2021). "Inducing Sparsity and Shrinkage in Time-Varying Parameter Models". Journal of Business & Economic Statistics, 39(3), 669-683.
Kalli, M., and Griffin, J. E. (2014). "Time-Varying Sparsity in Dynamic Regression Models". Journal of Econometrics, 178(2), 779-793.
Koop, G., and Korobilis, D. (2013). "Large Time-Varying Parameter VARs". Journal of Econometrics, 177(2), 185-198.
Koop, G., and Korobilis, D. (2012). "Forecasting Inflation using Dynamic Model Averaging". International Economic Review, 53(3), 867-886.

Bibliography:

Chan, J. C., Koop, G., Poirier, D. J., and Tobias, J.L. (2019). Bayesian Econometric Methods. Cambridge University Press.
Kilian, L., and Lütkepohl, H. (2017). Structural Vector Autoregressive Analysis. Cambridge University Press.
Herbst, E. P., and Schorfheide, F. (2016). Bayesian Estimation of DSGE Models. Princeton University Press.
Ibragimov, I. A., and Has' Minskii, R. Z. (2013). Statistical Estimation: Asymptotic Theory (Vol. 16). Springer Science & Business Media.
Ghosh, J. K., Delampady, M., and Samanta, T. (2007). An Introduction to Bayesian Analysis: Theory and Methods. Springer Science & Business Media.
Gamerman, D., and Lopes, H. F. (2006). Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Chapman and Hall/CRC.
Geweke, J. (2005). Contemporary Bayesian Econometrics and Statistics. John Wiley & Sons.
Bauwens, L., Lubrano, M., and Richard, J.F. (2000). Bayesian Inference in Dynamic Econometric Models. Oxford University Press.
White, H. (1996). Estimation, Inference and Specification Analysis. Cambridge University Press.
Hendry, D. F. (1995). Dynamic Econometrics. Oxford University Press.
Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press.

Optional Further Reading:

A. MCMC Methods and Applications

Laitinen, P., and Vihola, M. (2024). "An invitation to Adaptive Markov Chain Monte Carlo Convergence Theory". Preprint arXiv:2408.14903.
Woźniak, T. (2024). "Fast and Efficient Bayesian Analysis of Structural Vector Autoregressions Using the R Package bsvars". Preprint arXiv:2410.15090.
WrĂłblewska, J. (2024). "Identification of Structural Shocks in Bayesian VEC Models with Two-State Markov-Switching Heteroskedasticity". Preprint arXiv:2406.03053.
Rich, K. M. (2024). "Measuring the Effects of Fiscal Policy Shocks on US Output in a Markov-Switching Bayesian VAR". Available at SSRN 5049342.
Bruns, M., and Piffer, M. (2023). "A New Posterior Sampler for Bayesian Structural Vector Autoregressive Models". Quantitative Economics, 14(4), 1221-1250.
Goldman, J. V., Sell, T., and Singh, S. S. (2022). "Gradient-based Markov Chain Monte Carlo for Bayesian Inference with Non-Differentiable Priors". Journal of the American Statistical Association, 117(540), 2182-2193.
Lux, T. (2022). "Bayesian Estimation of Agent-based Models via Adaptive Particle Markov Chain Monte Carlo". Computational Economics, 60(2), 451-477.
Schorfheide, F., Song, D., and Yaron, A. (2018). "Identifying Long‐Run Risks: A Bayesian Mixed‐Frequency Approach". Econometrica, 86(2), 617-654.
Chib, S., and Ramamurthy, S. (2010). "Tailored Randomized Block MCMC Methods with Application to DSGE Models". Journal of Econometrics, 155(1), 19-38.
Müller, G. (2010). "MCMC Estimation of the COGARCH (1, 1) Model". Journal of Financial Econometrics, 8(4), 481-510.
Sims, C. A., Waggoner, D. F., and Zha, T. (2008). "Methods for Inference in Large Multiple-Equation Markov-Switching Models". Journal of Econometrics, 146(2), 255-274.
Fernández-Villaverde, J., and Rubio-Ramírez, J. F. (2007). "Estimating Macroeconomic Models: A Likelihood Approach". Review of Economic Studies, 74(4), 1059-1087.
Jacquier, E., Johannes, M., and Polson, N. (2007). "MCMC Maximum Likelihood for Latent State Models". Journal of Econometrics, 137(2), 615-640.
Roberts, G. O., and Rosenthal, J. S. (2006). "Harris Recurrence of Metropolis-within-Gibbs and Trans-Dimensional Markov Chains". Annals of Applied Probability, 16(4), 2123-2139.
Chernozhukov, V., and Hong, H. (2003). "An MCMC Approach to Classical Estimation". Journal of Econometrics, 115(2), 293-346.
He, X., and Hu, F. (2002). "Markov Chain Marginal Bootstrap". Journal of the American Statistical Association, 97(459), 783-795.
Eraker, B. (2001). "MCMC Analysis of Diffusion Models with Application to Finance". Journal of Business & Economic Statistics, 19(2), 177-191.
Gamerman, D. (1998). "Markov Chain Monte Carlo for Dynamic Generalised Linear Models". Biometrika, 215-227.
Green, P. J. (1995). "Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination". Biometrika, 82(4), 711-732.
Carter, C. K., and Kohn, R. (1994). "On Gibbs Sampling for State Space Models". Biometrika, 81(3), 541-553.
George, E. I., and McCulloch, R. E. (1993). "Variable Selection via Gibbs Sampling". Journal of the American Statistical Association, 88(423), 881-889.
Geyer, C. J. (1992). "Practical Markov Chain Monte Carlo". Statistical Science, 473-483.

B. Classical Identification of Cointegration

Zhang, R., Robinson, P., and Yao, Q. (2019). "Identifying Cointegration by Eigenanalysis". Journal of the American Statistical Association, 114(526), 916-927.
Mosconi, R., and Paruolo, P. (2017). "Identification Conditions in Simultaneous Systems of Cointegrating Equations with Integrated Variables of Higher Order". Journal of Econometrics, 198(2), 271-276.
Khalaf, L., and Urga, G. (2014). "Identification Robust Inference in Cointegrating Regressions". Journal of Econometrics, 182(2), 385-396.
Bierens, H.J., and Martins, L.F. (2010). "Time-Varying Cointegration". Econometric Theory, 26(5), 1453-1490.
Jacobs, J.P., and Wallis, K.F. (2010). "Cointegration, Long-Run Structural Modelling and Weak Exogeneity: Two Models of the UK Economy". Journal of Econometrics, 158(1), 108-116.
Johansen, S. (2010). "Some Identification Problems in the Cointegrated Vector Autoregressive Model". Journal of Econometrics, 158(2), 262-273.
Johansen, S. (2005). "Interpretation of Cointegrating Coefficients in the Cointegrated Vector Autoregressive Model". Oxford Bulletin of Economics and Statistics, 67(1), 93-104.
Chang, Y. (2000). "Vector Autoregressions with Unknown Mixtures of I (0), I (1), and I (2) Components". Econometric Theory, 16(6), 905-926.
Luukkonen, R., Ripatti, A., and Saikkonen, P. (1999). "Testing for a Valid Normalization of Cointegrating Vectors in Vector Autoregressive Processes". Journal of Business & Economic Statistics, 17(2), 195-204.
Saikkonen, P. (1999). "Testing Normalization and Overidentification of Cointegrating Vectors in Vector Autoregressive Processes". Econometric Reviews, 18(3), 235-257.
Boswijk, H.P. (1996). "Testing Identifiability of Cointegrating Vectors". Journal of Business & Economic Statistics, 14(2), 153-160.

C. Classical and Bayesian Approach to Cointegration and Unit Roots

Diniz, M.A., Pereira, C.A., and Stern, J.M. (2020). "Cointegration and Unit Root Tests: A Fully Bayesian Approach". Entropy, 22(9), 968.
Koop, G., Leon-Gonzalez, R., and Strachan, R. W. (2011). "Bayesian Inference in a Time Varying Cointegration Model". Journal of Econometrics, 165(2), 210-220.
Hoover, K.D., Johansen, S., and Juselius, K. (2008). "Allowing the Data to Speak Freely: The Macroeconometrics of the Cointegrated Vector Autoregression". American Economic Review, 98(2), 251-255.
Villani, M. (2006). "Bayesian Point Estimation of the Cointegration Space". Journal of Econometrics, 134(2), 645-664.
Villani, M. (2005). "Bayesian Inference of General Linear Restrictions on the Cointegration Space". Sveriges Riksbank Working Paper Series (No. 189). Available at SSRN 2025754.
Strachan, R.W., and Inder, B. (2004). "Bayesian Analysis of the Error Correction Model". Journal of Econometrics, 123(2), 307-325.
Strachan, R.W. (2003). "Valid Bayesian Estimation of the Cointegrating Error Correction Model". Journal of Business & Economic Statistics, 21(1), 185-195.
Kleibergen, F., and Paap, R. (2002). "Priors, Posteriors and Bayes Factors for a Bayesian Analysis of Cointegration". Journal of Econometrics, 111(2), 223-249.
Kleibergen, F., and van Dijk, H.K. (1998). "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures". Econometric Theory, 14(6), 701-743.
Lubrano, M. (1995). "Testing for Unit Roots in a Bayesian Framework". Journal of Econometrics, 69(1), 81-109.
Hoek, H., Lucas, A., and van Dijk, H.K. (1995). "Classical and Bayesian Aspects of Robust Unit Root Inference". Journal of Econometrics, 69(1), 27-59.
Kleibergen, F., and van Dijk, H.K. (1994). "On the Shape of the Likelihood/Posterior in Cointegration Models". Econometric Theory, 10(3-4), 514-551.
Schotman, P.C., and van Dijk, H.K. (1991). "On Bayesian Routes to Unit Roots". Journal of Applied Econometrics, 6(4), 387-401.

D. Classical and Bayesian Asymptotics

Ploberger, W., and Phillips, P. C. B. (2003). "Empirical Limits for Time Series Econometric Models". Econometrica, 71(2), 627-673.
Uhlig, H. (1997). "Bayesian Vector Autoregressions with Stochastic Volatility". Econometrica, 65(1), 59-73.
Phillips, P. C. B. (1996). "Econometric Model Determination". Econometrica, 64(4), 763-812.
Phillips, P. C. B., and Ploberger, W. (1996). "An Asymptotic Theory of Bayesian Inference for Time Series". Econometrica, 64(2), 381-412.

E. Bayesian Consistency and Semiparametric Approach

Breunig, C., Liu, R., and Yu, Z. (2024). "Semiparametric Bayesian Difference-in-Differences". Preprint arXiv:2412.04605.
Bickel, P.J., and Kleijn, B.J. (2012). "The Semiparametric Bernstein–von Mises Theorem". Annals of Statistics, 40(1), 206-237.
Kleijn, B.J., and van der Vaart, A.W. (2012). "The Bernstein-von-Mises Theorem under Misspecification". Electronic Journal of Statistics, 6, 354-381
Xing, Y., and Ranneby, B. (2009). "Sufficient Conditions for Bayesian Consistency". Journal of Statistical Planning and Inference, 139(7), 2479-2489.
Conley, T.G., Hansen, C.B., McCulloch, R.E., and Rossi, P. E. (2008). "A Semi-parametric Bayesian Approach to the Instrumental Variable Problem". Journal of Econometrics, 144(1), 276-305.
Lijoi, A., Prünster, I., and Walker, S.G. (2007). "Bayesian Consistency for Stationary Models". Econometric Theory, 23(4), 749-759.
Koop, G., Poirier, D. J., and Tobias, J. (2005). "Semiparametric Bayesian Inference in Multiple Equation Models". Journal of Applied Econometrics, 20(6), 723-747.
Koop, G., and Poirier, D. J. (2004). "Bayesian Variants of Some Classical Semiparametric Regression Techniques". Journal of Econometrics, 123(2), 259-282.
Walker, S. (2004). "New Approaches to Bayesian Consistency". Annals of Statistics, 32(5): 2028-2043.
Shen, X. (2002). "Asymptotic Normality of Semiparametric and Nonparametric Posterior Distributions". Journal of the American Statistical Association, 97(457), 222-235.

F. The Use of Prior, Posterior and Predictive Distributions

> Predictive Distribitions

Warne, A., Coenen, G., and Christoffel, K. (2013). "Predictive Likelihood Comparisons with DSGE and DSGE-VAR Models". ECB Working Paper (No. 1536).
Ando, T., and Tsay, R. (2010). "Predictive Likelihood for Bayesian Model Selection and Averaging". International Journal of Forecasting, 26(4), 744-763.

> Posterior Distribitions

Yiu, A., Fong, E., Holmes, C., and Rousseau, J. (2025). "Semiparametric Posterior Corrections". Journal of the Royal Statistical Society Series B, qkaf005.
Moya, B., and Walker, S.G. (2025). "Martingale Posterior Distributions for Time-Series Models". Statistical Science, 40(1), 68-80.
Fong, E., Holmes, C., and Walker, S.G. (2023). "Martingale Posterior Distributions". Journal of the Royal Statistical Society Series B, 85(5), 1357-1391.

> Prior Distribitions

Spezia, L. (2024). "Bayesian Prior Modelling in Vector Autoregressions via the Yule-Walker Equations". Communications in Statistics-Theory and Methods, 53(14), 5230-5247.
Prüser, J. (2023). "Data-based Priors for Vector Error Correction Models". International Journal of Forecasting, 39(1), 209-227.
Jarociński, M., and Marcet, A. (2019). "Priors about Observables in Vector Autoregressions". Journal of Econometrics, 209(2), 238-255.
Giannone, D., Lenza, M., and Primiceri, G.E. (2019). "Priors for the Long Run". Journal of the American Statistical Association, 114(526), 565-580.
Korobilis, D. (2016). "Prior Selection for Panel Vector Autoregressions". Computational Statistics & Data Analysis, 101, 110-120.

Kass, R.E., and Wasserman, L. (1996). "The Selection of Prior Distributions by Formal Rules". Journal of the American Statistical Association, 91(435), 1343-1370.

G. Further Topics On Bayesian Theory & Methods

> Quasi-Bayes

Müller, U. K., and Norets, A. (2024). "Locally Robust Efficient Bayesian Inference". Working paper (Submitted to Econometrica).
Andrews, I., and Mikusheva, A. (2022). "GMM is Inadmissible under Weak Identification". Preprint arXiv:2204.12462.
Kalli, M., and Griffin, J. E. (2018). "Bayesian Nonparametric Vector Autoregressive Models". Journal of Econometrics, 203(2), 267-282.

> Generalized Bayes

Astfalck, L., Bird, C., and Williamson, D. (2024). "Generalised Bayes Linear Inference". Preprint arXiv:2405.14145.
Fiksel, J., Datta, A., Amouzou, A., and Zeger, S. (2022). "Generalized Bayes Quantification Learning under Dataset Shift". Journal of the American Statistical Association, 117(540), 2163-2181.
Bissiri, P. G., Holmes, C. C., and Walker, S. G. (2016). "A General Framework for Updating Belief Distributions". Journal of the Royal Statistical Society Series B, 78(5), 1103-1130.

> Predictive Bayes

Barbieri, M. M., and Berger, J. O. (2004). "Optimal Predictive Model Selection". Annals of Statistics, 32(3), 870-897.
Laud, P. W., and Ibrahim, J. G. (1995). "Predictive Model Selection". Journal of the Royal Statistical Society Series B, 57(1), 247-262.

> Post-Bayes

Guedj, B. (2019). "A Primer on PAC-Bayesian Learning". Preprint arXiv:1901.05353.

Bibliography:

Särkkä, S., and Svensson, L. (2023). Bayesian Filtering and Smoothing (Vol. 17). Cambridge University Press.
Ghosal, S., and van der Vaart, A. W. (2017). Fundamentals of Nonparametric Bayesian Inference (Vol. 44). Cambridge University Press.
Rossi, P. (2014). Bayesian Non-and Semi-parametric Methods and Applications. Princeton University Press.
Hjort, N. L., Holmes, C., Müller, P., and Walker, S. G. (Eds.). (2010). Bayesian Nonparametrics (Vol. 28). Cambridge University Press.

TEACHING DURING THE ACADEMIC YEAR 2023/2024

Academic Institution: University of Helsinki
Academic Unit: Economics Division

During the 2023-2024 academic year, as a Postdoctoral Researcher at the Faculty of Social Sciences of the University of Helsinki, I had teaching responsibilities for the following course.

Spring 2024 (2nd teaching period)

Lecturer: Applied Macroeconometrics I, MSc/PhD level, University of Helsinki.

Module Syllabus (Preliminary).
Supplementary Material (Preliminary).

Problem Set 1 Problem Set 2

Problem Set 3 Problem Set 4

R Practical 1 R Practical 2

Assignment 1 Solution Example

Assignment 2 Solution Example

Intro to Probability & Statistics (2022/23)

Introduction to Probability & Statistics (7.5 ECTS)

During these lecturers we introduce the principles of probability and statistics which are considered as the building blocks for econometrics estimation, testing and inference.

Topic 1: Terminology and Descriptive Statistics

Topic 2: Foundations of Probability Slides with Advanced Topics

Topic 3: Discrete and Continuous Distributions

Topic 4: Sampling Distributions and Hypothesis Testing

Topic 5: Joint Distributions, Independence, Covariance and Correlation

Topic 6: Foundations of Time Series and Stochastic Processes

Module Description

The aim of the course is to facilitate students’ understanding on fundamental concepts of probability and statistics and their application to analyze empirical data related to economic and financial problems. The course outline includes, among others, the following concepts: descriptive statistics, probabilities, random variables, discrete distributions, continuous distributions, standard normal distribution, sampling distributions, confidence intervals, type I and II errors, hypothesis testing, contingency tables, independence conditions and tests, joint distributions, covariance and correlation measures, foundations of time series. The course consists of lectures and practical applications.

Handouts

Handout 1 Handout 2 Handout 3 Handout 4

Handout 5 Handout 6 Handout 7 Handout 8

Handout 9 Handout 10 Handout 11 Handout 12

Handout 13 Tutorial a Tutorial b

Problem Sets

Problem Set 4 Solutions

Problem Set 5 Solutions

Problem Set 6 Solutions

Problem Set 7 Solutions

Photo Credit: © Christis Katsouris (2010)

Applied Econometrics II (2022/23) co-taught with Dr Julian Dyer

Applied Econometrics II (7.5 ECTS)

Lecture Slides

Topic 1: Fundamentals & Univariate Time Series Models
Topic 2: Unit Roots, Cointegration and Structural Breaks
Topic 3: Multivariate Time Series Regression Models (VAR, Cointegrated VAR)
Topic 4: Nonlinear Time Series Models (Threshold, Switching, Garch)
Topic 5: Forecasting and Forecast Evaluation Applications
Topic 6: High Dimensional Time Series Models
Revision: Review Slides I Review Slides II Review Slides III

Computer Lab Workshops & Tutorials

Computer Lab 1: Notes 1a Notes1b Practical 1
Computer Lab 2: Notes 2a Notes2b Practical 2
Computer Lab 3: Notes 3 Practical 3
Computer Lab 4: Notes 4 Practical 4
Computer Lab 5: Notes 5 Practical 5

Empirical Applications for Assignment

Money Supply and Inflation: Construct a dataset which includes time series variables that characterize movements in the money supply and time series variables for inflation. Then, implement Granger-Causality test statistics based on suitable hypothesis testing formulations to study whether there are statistical evidence supporting the hypothesis of an instantaneous relation between money supply and inflation in an economy. Test statistics and critical values should be obtained under the null hypothesis of no instantaneous causality through time.
Unemployment Rate and Inflation Rate: Similar implementations to the example above. Recall that the main idea of the unit root test hypothesis is that the difference of an observed time series do not depend on its levels, or in other words, the levels of the time series have a unit root that can be removed by differencing (see, Nielsen, B. (2001, Ecta)).
Income Inequality Measures Across Countries: Another possible research project, is to construct an econometric framework for panel data regressions with the aim to study income inequality measures across countries. Depending on the set of regressors related econometric specifications are:
- Cointegrated Macroeconomic Variables: In this case, the relevant econometric specification is the panel data cointegrating regression model. Related research questions include to study the cointegration dynamics across the cross-section under the presence of structural instability or to study the impact of heterogeneous slopes across countries. From the econometrics point of view: (a) Panel Data Cointegration Testing with Structural Instabilities, or (b) Granger Non-Causality Testing in Panel Data Cointegrating Regressions.
- (Level) Stationary Macroeconomic Variables: In this case, a relevant econometric framework is to compare the estimation of fixed effects to random effects with panel data regressions for a cross-section of countries. The set of macroeconomic variables can include country-specific indicators such as gross domestic product, household consumption, inflation, corruption etc.

Related Literature (Updated July 2025)

A. Time Series Econometrics Literature:

1. Unit Roots, Structural Breaks and Cointegration

Sun, Y., and Wang, X. (2022). "An Asymptotically F-Distributed Chow Test in the Presence of Heteroscedasticity and Autocorrelation". Econometric Reviews, 41(2), 177-206.
Perron, P., Yamamoto, Y., and Zhou, J. (2020). "Testing Jointly for Structural Changes in the Error Variance and Coefficients of a Linear Regression Model". Quantitative Economics, 11(3), 1019-1057.
Maki, D. (2012). "Tests for Cointegration Allowing for an Unknown Number of Breaks". Economic Modelling, 29(5), 2011-2015.
Kejriwal, M., and Perron, P. (2010). "Testing for Multiple Structural Changes in Cointegrated Regression Models". Journal of Business & Economic Statistics, 28(4), 503-522.
Arai, Y., and Kurozumi, E. (2007). "Testing for the Null Hypothesis of Cointegration with a Structural Break". Econometric Reviews, 26(6), 705-739.
Steland, A. (2007). "Monitoring Procedures to Detect Unit Roots and Stationarity". Econometric Theory, 23(6), 1108-1135.
Zivot, E., and Andrews, D. W. K. (2002). "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis". Journal of Business & Economic Statistics, 20(1), 25-44.
Xiao, Z. (2001). "Testing the Null Hypothesis of Stationarity Against an Autoregressive Unit Root Alternative". Journal of Time Series Analysis, 22(1), 87-105.
Andrews, D. W. K. (1993). "Tests for Parameter Instability and Structural Change with Unknown Change Point". Econometrica, 61(4), 821-856.
Schwert, G. W. (1987). "Effects of Model Specification on Tests for Unit Roots in Macroeconomic Data". Journal of Monetary Economics, 20(1), 73-103.

2. Trend-Cycle Decomposition

Kamber, G., Morley, J., and Wong, B. (2025). "Trend-Cycle Decomposition in the Presence of Large Shocks". Journal of Economic Dynamics and Control, 173, 105066.
Blasques, F., van Brummelen, J., Gorgi, P., and Koopman, S. J. (2024). "A Robust Beveridge–Nelson Decomposition using a Score-driven Approach with an Application". Economics Letters, 236, 111588.
Morley, J., Tran, T. D., and Wong, B. (2024). "A Simple Correction for Misspecification in Trend-Cycle Decompositions with an Application to Estimating r". Journal of Business & Economic Statistics, 42(2), 665-680.
Tian, J., Jacobs, J. P., and Osborn, D. R. (2024). "Multivariate Trend‐Cycle Seasonal Decompositions with Correlated Innovations". Oxford Bulletin of Economics and Statistics, 86(5), 1260-1289.
Kamber, G., Morley, J., and Wong, B. (2018). "Intuitive and Reliable Estimates of the Output Gap from a Beveridge-Nelson Filter". Review of Economics and Statistics, 100(3), 550-566.
Morley, J., and Piger, J. (2008). "Trend/Cycle Decomposition of Regime-Switching Processes". Journal of Econometrics, 146(2), 220-226.
Romano, J. P., and Wolf, M. (2001). "Subsampling Intervals in Autoregressive Models with Linear Time Trend". Econometrica, 69(5), 1283-1314.
Clark, P. K. (1987). "The Cyclical Component of US Economic Activity". Quarterly Journal of Economics, 102(4), 797-814.

3. ARDL Models and Granger Causality Testing

> Testing Granger Causality in ARDL Models

Daly, H., et al. (2024). "The Dynamic Relationships between Oil Products Consumption and Economic Growth in Saudi Arabia: Using ARDL Cointegration and Toda-Yamamoto Granger Causality Analysis". Energy Strategy Reviews, 54, 101470.
Kripfganz, S., and Schneider, D. C. (2023). "ARDL: Estimating Autoregressive Distributed Lag and Equilibrium Correction Models". The Stata Journal, 23(4), 983-1019.

> Testing Granger Causality in Quantiles

Mayer, A., Wied, D., and Troster, V. (2025). "Quantile Granger Causality in the Presence of Instability". Journal of Econometrics, 249, 105992.
Bouezmarni, T., Doukali, M., and Taamouti, A. (2024). "Testing Granger Non-Causality in Expectiles". Econometric Reviews, 43(1), 30-51.
Troster, V. (2018). "Testing for Granger-Causality in Quantiles". Econometric Reviews, 37(8), 850-866.
Chen, Y. T. (2016). "Testing for Granger Causality in Moments". Oxford Bulletin of Economics and Statistics, 78(2), 265-288.
Candelon, B., and Tokpavi, S. (2016). "A Nonparametric Test for Granger Causality in Distribution with Application to Financial Contagion". Journal of Business & Economic Statistics, 34(2), 240-253.

4. Estimation Robust to Serial Correlation

Mohr, F. X. (2025). R Package 'prais': Prais-Winsten Estimator for AR(1) Serial Correlation. Available at r-project.
Moriya, K., and Noda, A. (2025). "A Note on the Asymptotic Properties of the GLS Estimator in Multivariate Regression with Heteroskedastic and Autocorrelated Errors". Preprint arXiv:2503.13950.
Nagakura, D. (2024). "Cochrane-Orcutt Type Estimator for Multivariate Linear Regression Model with Serially Correlated Errors". Available at SSRN 4951695.
Vougas, D. V. (2021). "Prais–Winsten Algorithm for Regression with Second or Higher Order Autoregressive Errors". Econometrics, 9(3), 32.
Thornton, D. L. (1987). "A Note on the Efficiency of the Cochrane-Orcutt Estimator of the AR (1) Regression Model". Journal of Econometrics, 36(3), 369-376.
Kobayashi, M. (1985). "Comparison of Efficiencies of Several Estimators for Linear Regressions with Autocorrelated Errors". Journal of the American Statistical Association, 80(392), 951-953.
Betancourt, R., and Kelejian, H. (1981). "Lagged Endogenous Variables and the Cochrane-Orcutt Procedure". Econometrica, 49(4), 1073-1078.
Hansen, L. P., and Hodrick, R. J. (1980). "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis". Journal of Political Economy, 88(5), 829-853.

5. Forecasting Applications

> Forecasting Univariate Time Series

Blasques, F., Koopman, S. J., and Artemova, M. (2024). "On the Use of Flexible Rolling-Window Estimation and Forecasting with Evidence from the Great Recession to the Covid-19 Pandemic". Available at SSRN 4954871.
Hannadige, S.B., Gao, J., Silvapulle, M.J., and Silvapulle, P. (2024). "Forecasting a Nonstationary Time Series using a Mixture of Stationary and Nonstationary Factors as Predictors". Journal of Business & Economic Statistics, 42(1), 122-134.
Cai, Z., and Juhl, T. (2023). "The Distribution of Rolling Regression Estimators". Journal of Econometrics, 235(2), 1447-1463.
Inoue, A., Jin, L., and Rossi, B. (2017). "Rolling Window Selection for Out-of-Sample Forecasting with Time-Varying Parameters". Journal of Econometrics, 196(1), 55-67.
Rossi, B., and Inoue, A. (2012). "Out-of-Sample Forecast Tests Robust to the Choice of Window Size". Journal of Business & Economic Statistics, 30(3), 432-453.
Pesaran, M. H., and Pick, A. (2011). "Forecast Combination Across Estimation Windows". Journal of Business & Economic Statistics, 29(2), 307-318.
Bai, J., and Ng, S. (2008). "Forecasting Economic Time Series using Targeted Predictors". Journal of Econometrics, 146(2), 304-317.
Marcellino, M., Stock, J. H., and Watson, M. W. (2006). "A Comparison of Direct and Iterated Multistep AR Methods for Forecasting Macroeconomic Time Series". Journal of Econometrics, 135(1-2), 499-526.
Ing, C. K. (2003). "Multistep Prediction in Autoregressive Processes". Econometric Theory, 19(2), 254-279.
Gospodinov, N. (2002). "Median Unbiased Forecasts for Highly Persistent Autoregressive Processes". Journal of Econometrics, 111(1), 85-101.
Clements, M. P., and Hendry, D. F. (1996). "Multi‐Step Estimation for Forecasting". Oxford Bulletin of Economics and Statistics, 58(4), 657-684.

> Forecasting Multivariate Time Series

Tu, Y., and Xie, X. (2023). "Forecasting Vector Autoregressions with Mixed Roots in the Vicinity of Unity". Econometric Reviews, 42(7), 556-585.
McAlinn, K., Aastveit, K. A., Nakajima, J., and West, M. (2020). "Multivariate Bayesian Predictive Synthesis in Macroeconomic Forecasting". Journal of the American Statistical Association, 115(531), 1092-1110.
Carriero, A., Kapetanios, G., and Marcellino, M. (2011). "Forecasting Large Datasets with Bayesian Reduced Rank Multivariate Models". Journal of Applied Econometrics, 26(5), 735-761.
Schorfheide, F. (2005). "VAR Forecasting under Misspecification". Journal of Econometrics, 128(1), 99-136.
Kilian, L. (2001). "Impulse Response Analysis in Vector Autoregressions with Unknown Lag Order". Journal of Forecasting, 20(3), 161-179.
Pesaran, H. H., and Shin, Y. (1998). "Generalized Impulse Response Analysis in Linear Multivariate Models". Economics Letters, 58(1), 17-29.

> Testing for Equal Predictive Accuracy

Akgün, O., Pirotte, A., Urga, G., and Yang, Z. (2025). "Testing Clustered Equal Predictive Ability with Unknown Clusters". Preprint arXiv:2507.14621.
Borup, D., et al. (2024). "The Anatomy of Out-of-Sample Forecasting Accuracy". FRB Atlanta Working Paper (No. 2022-16). Available at SSRN 4278745.
Coroneo, L., and Iacone, F. (2024). "Testing for Equal Predictive Accuracy with Strong Dependence". International Journal of Forecasting.
Kim, D. (2024). "On the Size Control of the Hybrid Test for Predictive Ability". Econometric Theory, 40(1), 213-232.
Hoga, Y., and Dimitriadis, T. (2023). "On Testing Equal Conditional Predictive Ability under Measurement Error". Journal of Business & Economic Statistics, 41(2), 364-376.
Li, J., Liao, Z., and Quaedvlieg, R. (2022). "Conditional Superior Predictive Ability". Review of Economic Studies, 89(2), 843-875.
Zhou, J., Li, H., and Zhong, W. (2021). "A Modified Diebold–Mariano Test for Equal Forecast Accuracy with Clustered Dependence". Economics Letters, 207, 110029.
Coroneo, L., and Iacone, F. (2020). "Comparing Predictive Accuracy in Small Samples using Fixed‐Smoothing Asymptotics". Journal of Applied Econometrics, 35(4), 391-409.
Zhu, Y., and Timmermann, A. (2020). "Can Two Forecasts have the same Conditional Expected Accuracy?". Preprint arXiv:2006.03238.
Hansen, P. R., and Timmermann, A. (2015). "Equivalence between Out‐of‐Sample Forecast Comparisons and Wald Statistics". Econometrica, 83(6), 2485-2505.
Clark, T. E., and McCracken, M. W. (2009). "Tests of Equal Predictive Ability with Real-Time Data". Journal of Business & Economic Statistics, 27(4), 441-454.
Giacomini, R., and White, H. (2006). "Tests of Conditional Predictive Ability". Econometrica, 74(6), 1545-1578.
West, K. D. (1996). "Asymptotic Inference about Predictive Ability". Econometrica, 64(5), 1067-1084.
Diebold, F. X., and Mariano, R. S. (1995). "Comparing Predictive Accuracy". Journal of Business & Economic Statistics, 20(1), 134-144.

Remark 1: Suppose that for the purpose of forecasting inflation we have two competing models, a benchmark regression model and a Lasso-based regression model. We are interested in checking that the differences in the forecasting performance among these two competing models are statistically significant. Exactly this is the purpose of the Giacomini-White statistical procedure. In other words, we can run pairwise Giacomini-White tests for equal predictive accuracy to infer about statistical significant differences on the predictive ability of these two models. Specifically, finding enough evidence to reject the null hypothesis implies that the Lasso-based models outperform the benchmark models. On the other hand, a drawback of these approaches is that must rely on rolling-window based forecasting schemes to avoid the variance degeneracy problem when testing for equal predictive accuracy, caused by competing models collapsing to the same model asymptotically (e.g., see discussion in Pitarakis (2023, arXiv:2312.16099) and Zhu & Timmermann (2020, arXiv:2006.03238)).

> Testing Predictive Ability with Cointegrated Data

Pitarakis, J. Y. (2025). "A Novel Approach to Predictive Accuracy Testing in Nested Environments". Econometric Theory, 41(1), 35-78.
Corradi, V., Swanson, N. R., and Olivetti, C. (2001). "Predictive Ability with Cointegrated Variables". Journal of Econometrics, 104(2), 315-358.

> Forecast Evaluation under Structural Change and Parameter Instability

Buccheri, G., Renò, R., and Vocalelli, G. (2025). "Taking Advantage of Biased Proxies for Forecast Evaluation". Journal of Econometrics, 251, 106068.
Goncalves, S., McCracken, M. W., and Yao, Y. (2025). "Bootstrapping Out-of-Sample Predictability Tests with Real-Time Data". Journal of Econometrics, 247, 105916.
Richter, S., and Smetanina, E. (2025). "Forecast Selection in Unstable Environments". Journal of Business & Economic Statistics, 1-13.
Hirano, K., and Wright, J. H. (2022). "Analyzing Cross-Validation for Forecasting with Structural Instability". Journal of Econometrics, 226(1), 139-154.
Boot, T., and Pick, A. (2020). "Does Modeling a Structural Break Improve Forecast Accuracy?". Journal of Econometrics, 215(1), 35-59.
Giacomini, R., and Rossi, B. (2010). "Forecast Comparisons in Unstable Environments". Journal of Applied Econometrics, 25(4), 595-620.
Pesaran, M. H., and Timmermann, A. (2007). "Selection of Estimation Window in the Presence of Breaks". Journal of Econometrics, 137(1), 134-161.
Inoue, A., and Kilian, L. (2005). "In-Sample or Out-of-Sample Tests of Predictability: Which One Should We Use?". Econometric Reviews, 23(4), 371-402.
Inoue, A., and Rossi, B. (2005). "Recursive Predictability Tests for Real-Time Data". Journal of Business & Economic Statistics, 23(3), 336-345.
Rossi, B. (2005). "Optimal Tests for Nested Model Selection with Underlying Parameter Instability". Econometric theory, 21(5), 962-990.

> Forecast Evaluation and Encompassing

Pitarakis, J. Y. (2023). "Direct Multi-Step Forecast based Comparison of Nested Models via an Encompassing Test". Preprint arXiv:2312.16099.
Gonçalves, S., McCracken, M. W., and Perron, B. (2017). "Tests of Equal Accuracy for Nested Models with Estimated Factors". Journal of Econometrics, 198(2), 231-252.
Clark, T. E., and McCracken, M. W. (2015). "Nested Forecast Model Comparisons: A New Approach to Testing Equal Accuracy". Journal of Econometrics, 186(1), 160-177.
Mariano, R. S., and Preve, D. (2012). "Statistical Tests for Multiple Forecast Comparison". Journal of Econometrics, 169(1), 123-130.
McCracken, M. W. (2007). "Asymptotics for Out of Sample Tests of Granger Causality". Journal of Econometrics, 140(2), 719-752.
Clark, T. E., and West, K. D. (2007). "Approximately Normal Tests for Equal Predictive Accuracy in Nested Models". Journal of Econometrics, 138(1), 291-311.
Clark, T. E., and McCracken, M. W. (2001). "Tests of Equal Forecast Accuracy and Encompassing for Nested Models". Journal of Econometrics, 105(1), 85-110.
Clements, M. P., and Hendry, D. F. (1993). "On the Limitations of Comparing Mean Square Forecast Errors". Journal of Forecasting, 12(8), 617-637.

> Model Selection and Model Averaging Methods

Chen, Y. T., Liu, C. A., and Su, J. H. (2025). "Bregman Model Averaging for Forecast Combination". Journal of Econometrics, 251, 106076.
Lin, T. C., and Liu, C. A. (2025). "Model Averaging Prediction for Possibly Nonstationary Autoregressions". Journal of Econometrics, 249, 105994.
Chen, Q., Hong, Y., and Li, H. (2024). "Time-Varying Forecast Combination for Factor-Augmented Regressions with Smooth Structural Changes". Journal of Econometrics, 240(1), 105693.
Hounyo, U., and Lahiri, K. (2023). "Estimating the Variance of a Combined Forecast: Bootstrap-based Approach". Journal of Econometrics, 232(2), 445-468.
Kejriwal, M., Nguyen, L., and Yu, X. (2023). "Multistep Forecast Averaging with Stochastic and Deterministic Trends". Econometrics, 11(4), 28.
Kejriwal, M., and Yu, X. (2021). "Generalized Forecast Averaging in Autoregressions with a Near Unit Root". The Econometrics Journal, 24(1), 83-102.
Pesaran, M. H., Pick, A., and Pranovich, M. (2013). "Optimal Forecasts in the Presence of Structural Breaks". Journal of Econometrics, 177(2), 134-152.
Patton, A. J., and Timmermann, A. (2007). "Properties of Optimal Forecasts under Asymmetric Loss and Nonlinearity". Journal of Econometrics, 140(2), 884-918.
Bhansali, R. J. (1996). "Asymptotically Efficient Autoregressive Model Selection for Multistep Prediction". Annals of the Institute of Statistical Mathematics, 48, 577-602.

6. Nonlinear Time Series Models

> Threshold and Markov-Switching Models

Giannerini, S., Goracci, G., and Rahbek, A. (2024). "The Validity of Bootstrap Testing for Threshold Autoregression". Journal of Econometrics, 239(1), 105379.
Hidalgo, J., Lee, J., and Seo, M. H. (2019). "Robust Inference for Threshold Regression Models". Journal of Econometrics, 210(2), 291-309.
Li, D., and Ling, S. (2012). "On the Least Squares Estimation of Multiple-Regime Threshold Autoregressive Models". Journal of Econometrics, 167(1), 240-253.
Li, J. (2006). "Testing Granger Causality in the Presence of Threshold Effects". International Journal of Forecasting, 22(4), 771-780.
Gonzalo, J., and Wolf, M. (2005). "Subsampling Inference in Threshold Autoregressive Models". Journal of Econometrics, 127(2), 201-224.
Lanne, M., and Saikkonen, P. (2002). "Threshold Autoregressions for Strongly Autocorrelated Time Series". Journal of Business & Economic Statistics, 20(2), 282-289.

> GARCH Models

Lanne, M., and Saikkonen, P. (2007). "A Multivariate Generalized Orthogonal Factor GARCH Model". Journal of Business & Economic Statistics, 25(1), 61-75.
Lundbergh, S., and Teräsvirta, T. (2002). "Evaluating GARCH Models". Journal of Econometrics, 110(2), 417-435.

7. LASSO-Based Time Series Models

Chudik, A., Pesaran, M. H., and Sharifvaghefi, M. (2024). "Variable Selection in High Dimensional Linear Regressions with Parameter Instability". Journal of Econometrics, 246(1-2), 105900.
Medeiros, M. C., and Mendes, E. F. (2017). "Adaptive LASSO Estimation for ARDL Models with GARCH Innovations". Econometric Reviews, 36(6-9), 622-637.
Yoon, Y. J., Lee, S., and Lee, T. (2017). "Adaptive LASSO for Linear Regression Models with ARMA-GARCH Errors". Communications in Statistics-Simulation and Computation, 46(5), 3479-3490.

B. Panel Data Econometrics Literature:

> Testing Granger Non-Causality in Panel Data Models

Xiao, J., Karavias, Y., Juodis, A., Sarafidis, V., and Ditzen, J. (2023). "Improved Tests for Granger Non-Causality in Panel Data". The Stata Journal, 23(1), 230-242.
Juodis, A., Karavias, Y., and Sarafidis, V. (2021). "A Homogeneous Approach to Testing for Granger Non-Causality in Heterogeneous Panels". Empirical Economics, 60(1), 93-112.

Dumitrescu, E. I., and Hurlin, C. (2012). "Testing for Granger Non-Causality in Heterogeneous Panels". Economic Modelling, 29(4), 1450-1460.

> Panel Data Cointegration Models

Banerjee, A., and Carrion-i-Silvestre, J. L. (2025). "Panel Data Cointegration Testing with Structural Instabilities". Journal of Business & Economic Statistics, 43(1), 122-133.
Lee, Y., Phillips, P.C.B., Song, S., and Sul, D. (2025). "Identifying Common Trend Determinants in Panel Data". Working Paper.
Westerlund, J., and Edgerton, D. L. (2008). "A Simple Test for Cointegration in Dependent Panels with Structural Breaks". Oxford Bulletin of Economics and Statistics, 70(5), 665-704.
Westerlund, J. (2008). "Panel Cointegration Tests of the Fisher Effect". Journal of Applied Econometrics, 23(2), 193-233.

> Forecasting with Panel Data Models

Pesaran, M. H., Pick, A., and Timmermann, A. (2024). "Forecasting with Panel Data: Estimation Uncertainty versus Parameter Heterogeneity". Preprint arXiv:2404.11198.
Qu, R., Timmermann, A., and Zhu, Y. (2024). "Comparing Forecasting Performance with Panel Data". International Journal of Forecasting, 40(3), 918-941.
Qu, R., Timmermann, A., and Zhu, Y. (2023). "Comparing Forecasting Performance in Cross-Sections". Journal of Econometrics, 237(2), 105186.
Liu, L., Moon, H. R., and Schorfheide, F. (2023). "Forecasting with Panel Tobit Model". Quantitative Economics, 14(1), 117-159.
Liu, L., Moon, H. R., and Schorfheide, F. (2020). "Forecasting with Dynamic Panel Data Models". Econometrica, 88(1), 171-201.
Greenaway-McGrevy, R. (2019). "Asymptotically Efficient Model Selection for Panel Data Forecasting". Econometric Theory, 35(4), 842-899.
Smith, S. C., Timmermann, A., and Zhu, Y. (2019). "Variable Selection in Panel Models with Breaks". Journal of Econometrics, 212(1), 323-344.
Greenaway-McGrevy, R. (2013). "Multistep Prediction of Panel Vector Autoregressive Processes". Econometric Theory, 29(4), 699-734.
Issler, J. V., and Lima, L. R. (2009). "A Panel Data Approach to Economic Forecasting: The Bias-Corrected Average Forecast". Journal of Econometrics, 152(2), 153-164.

> Unbalanced Panel Data Models

Baltagi, B. H., and Liu, L. (2020). "Forecasting with Unbalanced Panel Data". Journal of Forecasting, 39(5), 709-724.
Atak, A., Linton, O., and Xiao, Z. (2011). "A Semiparametric Panel Model for Unbalanced Data with Application to Climate Change in the United Kingdom". Journal of Econometrics, 164(1), 92-115.

> Nonlinear Panel Data Models

Gonzalez, A., Teräsvirta, T., Van Dijk, D., and Yang, Y. (2017). "Panel Smooth Transition Regression Models". Working paper.

C. Applied Econometrics Literature:

Ascari, G., and Fosso, L. (2024). "The International Dimension of Trend Inflation". Journal of International Economics, 148, 103896.
Schüler, Y. S. (2024). "Filtering Economic Time Series: On the Cyclical properties of Hamilton's Regression Filter and the Hodrick-Prescott Filter". Review of Economic Dynamics, 54, 101237.
Biolsi, C. (2023). "Do the Hamilton and Beveridge–Nelson Filters provide the same Information about Output Gaps? An Empirical Comparison for Practitioners". Journal of Macroeconomics, 75, 103496.
McNown, R., Sam, C. Y., and Goh, S. K. (2018). "Bootstrapping the Autoregressive Distributed Lag Test for Cointegration". Applied Economics, 50(13), 1509-1521.
Balcilar, M., Gupta, R., and Miller, S. M. (2015). "Regime Switching Model of US Crude Oil and Stock Market Prices: 1859 to 2013". Energy Economics, 49, 317-327.
Asteriou, D., Dimelis, S., and Moudatsou, A. (2014). "Globalization and Income Inequality: A Panel Data Econometric Approach for the EU27 Countries". Economic Modelling, 36, 592-599.
Lin, P. C., and Huang, H. C. (2012). "Convergence in Income Inequality? Evidence from Panel Unit Root Tests with Structural Breaks". Empirical Economics, 43, 153-174.
Luginbuhl, R., and Koopman, S. J. (2004). "Convergence in European GDP Series: A Multivariate Common Converging Trend–Cycle Decomposition". Journal of Applied Econometrics, 19(5), 611-636.

Bibliography:

Neusser, K. (2016). Time Series Econometrics. Springer.
Koopman, S. J., and Shephard, N. (2015). Unobserved Components and Time Series Econometrics. Oxford University Press.
Martin, V., Hurn, S., and Harris, D. (2013). Econometric Modelling with Time Series: Specification, Estimation and Testing. Cambridge University Press.
Enders, W. (2008). Applied Econometric Time Series. John Wiley & Sons.

Kleiber, C., and Zeileis, A. (2008). Applied Econometrics with R. Springer Science & Business Media.

Photo Credit: © Christis Katsouris (2023)

Advanced Econometrics with Machine Learning Applications

* Teaching material prepared during the academic year 2022/2023.

Second Year MRes/PhD Course

Last updated: April 2025.

The module is inspired by the "Advanced Statistical Methods for Econometrics" approach, with a modern perspective which is in the intersection of Econometric Methods for Big Data and Time Series Econometrics with Machine Learning Applications. We focus on high-dimensional econometrics and machine learning applications.

Design: Original curriculum design by Dr. Christis Katsouris, based on state-of-the-art developments in econometrics and machine learning. Dr. Katsouris has extensive experience with designing innovative teaching material and proposing novel curriculum for advanced modules in econometrics, through original research activities as well as co-organization of Reading Group sessions on topics spanning the fields of Econometrics, Time Series Analysis and Machine Learning. Recently, advanced courses in Economics and Econometrics such as MRes in Economics which have two-year duration for a start during the upcoming academic year 2025/2026, have now moved towards similar directions of teaching and delivery of related learning objectives.
Contributions: An original econometrics class proposed and designed by Dr. Christis Katsouris. The course provides a new linkage between time series econometrics and microeconometrics by simultaneously and jointly introducing aspects to cross-section data (as discussed in applied microeconometrics) such that we allow for general forms of cross-sectional dependence (without introducing the weak and strong cross-section dependence), thereby extending more conventional approaches to static and dynamic panel data analysis with i.i.d, non-i.i.d or clustered observations, for both stationary and non-stationary time series, where high-dimensionality is allowed.
Prerequisites: This module requires passing Econometrics I & Econometrics II from an MRes/PhD in Economics program which has both taught and research stages.

Recommended Textbooks:

Hansen, B. (2022). Econometrics. Princeton University Press.
Chan, F., and Mátyás, L. (2022). Econometrics with Machine Learning. Springer Press.
Hayashi, F. (2011). Econometrics. Princeton University Press.
Baltagi, B.H. (2008). Econometric Analysis of Panel Data. Wiley Press.

Module Synopsis:

We review recent methodological developments from the econometrics and machine learning literature for applications to both time series data as well as cross-sectional data. Specifically, we review applications commonly used for the econometric analysis of cross-sectional data as well as applications and related methodologies for the econometric analysis of macroeconomic and financial data. In particular, in the empirical finance and asset pricing literature, large cross sections correspond to stock returns of n firms which are assumed to be independent observations. Moreover, for applications with time series data recall that error terms in time series regressions can be either i.i.d or non-i.i.d such as in the case of heteroscedastic errors (which implies a time-dependent variance of the time series process). To this end, we also discuss the notion of martingale difference sequence as well as related testing validity procedures. Lastly, we discuss the notion of endogeneity in econometric models which corresponds to the setting where regressors are correlated with the error term of the observed target variable. Although the study of endogeneity requires a different set of assumptions as well as econometric estimation and testing approaches for cross-sectional data versus time series data.

Cross-sectional data: The case of cross-sectional observations (observed at a fixed time, i.e., no time-index), has many interesting applications in econometrics. In the applied microeconometrics literature estimation and inference methods correspond to the case of independently and identically distributed cross-sectional units (such as consumers' expenditures or household labour supply). We focus on causal inference techniques using econometric models and data from quasi-experimental studies (empirical studies used to estimate the causal effect of an intervention). We discuss two applications from the financial economics literature, namely 'The Out-of-Town Housing Experiment' and a quasi-experimental study related to deposit insurance. Further examples, include the follow-up of outcome measurements of study participants through 'waves', in which case econometric modelling is based on longitudinal data/repeated cross-sectional samples (such as in the case of social mobility studies). A high-dimensional environment here corresponds to a setting where the number of cross-sectional units are much larger than the time series observations, while keeping the number of regressors fixed.

Time-series data: In the time series econometrics literature we study separately the case of models with a univariate dependent variable (scalar) versus the case of a multivariate dependent variable (vector). The former setting includes the case of a scalar dependent variable with multiple regressors (multiple time series regression) while the latter setting corresponds to multivariate time series modelling (VAR models). Here, we use single-equation models and focus on studying the properties of the underline stochastic processes such as the cases of stationary, near nonstationary and nonstationary regressors. In general, time series regression models can have either i.i.d error terms or serially dependent error terms (such as an AR(1) error term). Moreover, we also permit the number of regressors to be high-dimensional (p much larger than the sample size n). Examples of related applications include: (i) Large datasets with macroeconomic variables, which is suitable for predictive regression models with high-dimensional regressors, or (ii) Panel datasets with time series observations, such that when we have n cross-sectional observations and T time series observations (static versus dynamic panel specifications). The case of serially dependent innovations in the context of time series regressions is also discussed. We discuss two applications from the financial economics literature, namely the predictability of banking crises and the predictive power of macroeconomic variables.

Econometric Theory: Although in this module we shall not extensively cover statistical and probability theory, is worth emphasizing that the literature which deals with weak convergence results for high-dimensional vectors of nearly nonstationary time series is limited, but nevertheless of independent interest to deeper our understanding of estimation and inference techniques. Existing theoretical results with respect to the use of Gaussian approximations for functionals of empirical processes within high-dimensional environments, usually employ different tools than the martingale approximation results commonly used in nonstationary econometrics.

The number of regressors with respect to the sample size is a crucial condition in all aforementioned examples (since we focus on high-dimensionality issues). Usually, related conditions, in such high-dimensional environments, are imposed on the rate of convergence of regressors with respect to the sample size, as well as with respect to the sparsity index. We consider applications covering both cross-sectional regressions and time-series regressions, especially with respect to the econometric methods for the following three Parts. For our econometric analyses we exclude cases where cross-sectional data have higher-order serial correlation dynamics or cases when panel time series data have cross-sectional dependence (which would require to impose additional factor dependence structures). The validity of classical HAC estimators for long-run covariance matrices in the current nonstandard setting with growing dimension requires special attention. We focus on (linear) regression models in possibly high-dimensional settings with either independent or time series data, such that the presence of heteroscedasticity is not completely ruled out. For example, in nearly nonstationary predictive regression models, the presence of heteroscedasticity has different effects on the limiting distributions of model estimators and test statistics depending on the degree of persistence of regressors. In high-dimensional settings these issues are worth further discussion and study. Lastly, we will discuss the notion of uniform inference for high-dimensional data, although those definitions have slightly different interpretation in the case of stationary time series versus nearly nonstationary time series, regardless of whether we have iid or dependent data. The fundamental difference between a finite-sample theory and an asymptotic approximation will be discussed with illustrative examples.

However, for this module we are not discussing the literature on vector autoregression models in order to cover in more depth the topics discussed above. Forecasting applications are also excluded. Emphasis is given on the following issues: (i) modeling techniques in the analysis of cross-section, panel and time series economic data, (ii) econometric inference techniques for addressing empirical research questions of interest, and (iii) asymptotic and econometric theory for model estimators and related test statistics across the applications discussed in Part A, B and C. We cover state-of-the-art aspects from the econometrics and machine learning literature, which should provide the impetus for independent academic research after completing this module.

Related Lecture Notes:

Katsouris, C. (2023). "Optimal Estimation Methodologies for Panel Data Regression Models". Preprint arXiv:2311.03471.
Katsouris, C. (2023). "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods". Preprint arXiv:2308.16192.
Katsouris, C. (2023). "Limit Theory under Network Dependence and Nonstationarity". Preprint arXiv:2308.01418.
Katsouris, C. (2023). "Quantile Time Series Regression Models Revisited". Preprint arXiv:2308.06617.

Part A. Cross-Section and Panel Data Econometrics with Machine Learning

Large sample analysis of model estimators & asymptotic theory tools
Inference in regression models estimated from cross-section data
Inference in regression models estimated from time series data
Generalized Method of Moments & IV estimation

Part B. Causal Inference in Econometrics with Machine Learning

Identification of Average Treatment Effects
Estimation & Inference Methods for Causal Effects
Double Robustness Methods & Applications

Part C. Machine Learning in Time Series Econometrics

Shrinkage Regression Methods
Variable and Model Selection Techniques
High Dimensional Predictive Regressions

Bibliography:

Hansen, B. (2022). Econometrics. Princeton University Press.
Chan, F., and Mátyás, L. (2022). Econometrics with Machine Learning. Springer Press.
Anatolyev, S., and Gospodinov, N. (2011). Methods for Estimation and Inference in Modern Econometrics. CRC Press.
Hayashi, F. (2011). Econometrics. Princeton University Press.
Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data. MIT Press.
Baltagi, B. H. (2008). Econometric Analysis of Panel Data. Wiley Press.

Davidson, R., and MacKinnon, J. G. (2004). Econometric Theory and Methods. Oxford University Press.
White, H. (2001). Asymptotic Theory for Econometricians. Academic Press.
Davidson, J. (1994). Stochastic Limit Theory: An Introduction for Econometricians. Oxford University Press.
Davidson, R., and MacKinnon, J. G. (1993). Estimation and Inference in Econometrics. Oxford University Press.

I. Causal Inference with Machine Learning Applications

a. Treatment Effects with High Dimensional Data

Semenova, V., Goldman, M., Chernozhukov, V., and Taddy, M. (2023). "Inference on Heterogeneous Treatment Effects in High‐Dimensional Dynamic Panels under Weak Dependence". Quantitative Economics, 14(2), 471-510.
Shen, D., Ding, P., Sekhon, J., and Yu, B. (2023). "Same Root Different Leaves: Time Series and Cross‐Sectional Methods in Panel Data". Econometrica, 91(6), 2125-2154.
Fan, Q., Hsu, Y.C., Lieli, R.P., and Zhang, Y. (2022). "Estimation of Conditional Average Treatment Effects with High-Dimensional Data". Journal of Business & Economic Statistics, 40(1), 313-327.
Colangelo, K., and Lee, Y.Y. (2020). "Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments". Preprint arXiv:2004.03036.
De Chaisemartin, C., and d’Haultfoeuille, X. (2020). "Two-way Fixed Effects Estimators with Heterogeneous Treatment Effects". American Economic Review, 110(9), 2964-2996.
Chernozhukov, V., et al. (2018). "Double/Debiased Machine Learning for Treatment and Structural Parameters". The Econometrics Journal, 21(1),1-68.
Abrevaya, J., Hsu, Y.C., and Lieli, R.P. (2015). "Estimating Conditional Average Treatment Effects". Journal of Business & Economic Statistics, 33(4), 485-505.
Farrell, M.H. (2015). "Robust Inference on Average Treatment Effects with Possibly more Covariates than Observations". Journal of Econometrics, 189(1), 1-23.

b. Program Evaluation with High Dimensional Data

Menchetti, F., Cipollini, F., and Mealli, F. (2023). "Combining Counterfactual Outcomes and ARIMA Models for Policy Evaluation". The Econometrics Journal, 26(1), 1-24.
Knaus, M.C. (2022). "Double Machine Learning-based Programme Evaluation under Unconfoundedness". The Econometrics Journal, 25(3), 602-627.
Ngueyep, R., and Serban, N. (2018). "High-Dimensional Multivariate Additive Regression for Uncovering Contributing Factors to Healthcare Expenditure". Biostatistics, 19(3), 359-373.
Semenova, V. (2018). "Machine Learning for Dynamic Discrete Choice". Preprint arXiv:1808.02569.

c. Quasi-Experimental Studies and Applications

Abadie, A., Athey, S., Imbens, G.W., and Wooldridge, J.M. (2023). "When Should you adjust Standard Errors for Clustering?". Quarterly Journal of Economics, 138(1), 1-35.
Anderson, H., Richardson, G., and Yang, B. (2023). "Deposit Insurance and Depositor Monitoring: Quasi‐Experimental Evidence from the Creation of the Federal Deposit Insurance Corporation". Journal of Money, Credit and Banking, 55(2-3), 441-464.
Deng, Y., Liao, L., Yu, J., and Zhang, Y. (2022). "Capital Spillover, House Prices, and Consumer Spending: Quasi-Experimental Evidence from House Purchase Restrictions". Review of Financial Studies, 35(6), 3060-3099.
Miller, S., and Soo, C.K. (2021). "Do Neighborhoods Affect the Credit Market Decisions of Low-Income Borrowers? Evidence from the Moving to Opportunity Experiment". Review of Financial Studies, 34(2), 827-863.

d. Financial Education Programs Studies

Golosov, M., Graber, M., Mogstad, M., and Novgorodsky, D. (2024). "How Americans Respond to Idiosyncratic and Exogenous Changes in Household Wealth and Unearned Income". Quarterly Journal of Economics, 139(2), 1321-1395.
Kaiser, T., Lusardi, A., Menkhoff, L., and Urban, C. (2022). "Financial Education Affects Financial Knowledge and Downstream Behaviors". Journal of Financial Economics, 145(2), 255-272.
Sekita, S., Kakkar, V., and Ogaki, M. (2022). "Wealth, Financial Literacy and Behavioral Biases in Japan: The Effects of Various Types of Financial Literacy". Journal of the Japanese and International Economies, 64, 101190.
Behrman, J.R., Mitchell, O.S., Soo, C.K., and Bravo, D. (2012). "How Financial Literacy Affects Household Wealth Accumulation". American Economic Review, 102(3), 300-304.

e. Triple Difference Designs Estimation

Caron, L. (2025). "Triple Difference Designs with Heterogeneous Treatment Effects". Preprint arXiv:2502.19620.

II. Time Series Data with Machine Learning

a. Stationary Time Series

Margaritella, L., and Sessinou, R. (2025). Precision Least Squares: Estimation and Inference in High-Dimensions. Journal of Business & Economic Statistics, 1-26.
Babii, A., Ghysels, E., and Striaukas, J. (2024). High-Dimensional Granger Causality Tests with an Application to VIX and News. Journal of Financial Econometrics, 22(3), 605-635.
Li, J., and Yan, H. (2024). Uniform Inference in High-Dimensional Threshold Regression Models. Preprint arXiv:2404.08105.
Adamek, R., Smeekes, S., and Wilms, I. (2023). Lasso Inference for High-Dimensional Time Series. Journal of Econometrics, 235(2), 1114-1143.
Gupta, A., and Seo, M.H. (2023). Robust Inference on Infinite and Growing Dimensional Time‐Series Regression. Econometrica, 91(4), 1333-1361.
Tonini, S., Chiaromonte, F., and Giovannelli, A. (2023). On the Impact of Serial Dependence on Penalized Regression Methods. Preprint arXiv:2208.00727.
Sattarhoff, C., and Spindler, M. (2022). High-Dimensional Time Series Regressions With HAC and HAR Penalty Loadings. Available at SSRN 4296969.
Yousuf, K., and Ng, S. (2021). Boosting High Dimensional Predictive Regressions with Time Varying Parameters. Journal of Econometrics, 224(1), 60-87.
Poignard, B., and Fermanian, J. D. (2021). High-Dimensional Penalized ARCH Processes. Econometric Reviews, 40(1), 86-107.
Chiou, H. T., Guo, M., and Ing, C.K. (2020). Variable Selection for High-Dimensional Regression Models with Time Series and Heteroscedastic Errors. Journal of Econometrics, 216(1), 118-136.
Li, Z., and Yao, J. (2019). Testing for Heteroscedasticity in High-Dimensional Regressions. Econometrics and Statistics, 9, 122-139.
Chan, N. H., Yau, C. Y., and Zhang, R. M. (2015). LASSO Estimation of Threshold Autoregressive Models. Journal of Econometrics, 189(2), 285-296.
Chang, J., Chen, S.X., and Chen, X. (2015). High Dimensional Generalized Empirical Likelihood for Moment Restrictions with Dependent Data. Journal of Econometrics, 185(1), 283-304.

b. Stationary Cointegrated Time Series

Hauzenberger, N., Pfarrhofer, M., and Rossini, L. (2025). Sparse Time-Varying parameter VECMs with an Application to Modeling Electricity Prices. International Journal of Forecasting, 41(1), 361-376.
Chen, H., and Lee, J. H. (2024). Predictive Quantile Regression with High-Dimensional Predictors: The Variable Screening Approach. Preprint arXiv:2410.15097.
Fan, R. Lee, J. H., and Shin, Y. (2023). Predictive Quantile Regression with Mixed Roots and Increasing Dimensions: The ALQR Approach. Journal of Econometrics, 237(2), 105372.
Fang, P., Gao, Z., and Tsay, R.S. (2023). Determination of the Effective Cointegration Rank in High-Dimensional Time-Series Predictive Regressions. Preprint arXiv:2304.12134.
Koo, B., Anderson, H.M., Seo, M. H., and Yao, W. (2020). High-Dimensional Predictive Regression in the Presence of Cointegration. Journal of Econometrics, 219(2), 456-477.
Liao, Z., and Phillips, P.C.B. (2015). Automated Estimation of Vector Error Correction Models. Econometric Theory, 31(3), 581-646.

c. Nearly Nonstationary Time Series

Gao, Z., Lee, J.H., Mei, Z., and Shi, Z. (2024). Econometric Inference for High Dimensional Predictive Regressions. Preprint arXiv:2409.10030.
Mei, Z., and Shi, Z. (2024). On LASSO for High Dimensional Predictive Regression. Journal of Econometrics (forthcoming).
Lee, J.H., Shi, Z., and Gao, Z. (2022). On LASSO for Predictive Regression. Journal of Econometrics, 229(2), 322-349.

III. Panel Data with Machine Learning

a. Stationary Time Series

Gao, J., Liu, F., Peng, B., and Yan, Y. (2025). Panel Data Estimation and Inference: Homogeneity versus Heterogeneity. Preprint arXiv:2502.03019.
Gao, J., Peng, B., and Yan, Y. (2024). Robust Inference for High-Dimensional Panel Data Models. Preprint arXiv:2405.07420.
Cheng, T., Dong, C., Gao, J., and Linton, O. (2024). GMM Estimation for High-Dimensional Panel Data Models. Journal of Econometrics, 244(1), 105853.
Carrasco, M., and Nayihouba, A. (2024). Regularized Estimation of Dynamic Panel Models. Econometric Theory, 40(2), 360-418.
Kock, A.B., and Tang, H. (2019). Uniform Inference in High-Dimensional Dynamic Panel Data Models with Approximately Sparse Fixed Effects. Econometric Theory, 35(2), 295-359.
Carvalho, C., Masini, R., and Medeiros, M.C. (2018). ArCo: An Artificial Counterfactual Approach for High-Dimensional Panel Time-series Data. Journal of Econometrics, 207(2), 352-380.

b. Nearly Nonstationary Time Series

Katsouris, C. (2025+). Inference in High-Dimensional Panel Data Predictive Regression Models. Work in progress.
Katsouris, C. (2025+). Robust Econometric Inference for LASSO Panel Data Predictive Regressions. Work in progress.
Liao, C., Mei, Z., and Shi, Z. (2024). Nickell Meets Stambaugh: A Tale of Two Biases in Panel Predictive Regressions. Preprint arXiv:2410.09825.
Masini, R., and Medeiros, M.C. (2021). Counterfactual Analysis with Artificial Controls: Inference, High Dimensions, and Nonstationarity. Journal of the American Statistical Association, 116(536), 1773-1788.

IV. Cross-Sectional Data with Machine Learning

a. Linear Mean Regressions

> Error Structure: iid sequences

Feng, Q., Jaidee, S., and Wang, W. (2025). "Robust Inference with High-Dimensional Instruments". Preprint arXiv:2506.23834v1.
Dou, L., Min, P., Wang, W., and Zhang, Y. (2025). "An Improved Inference for IV Regressions". Preprint arXiv:2506.23816.
Liu, W., Lin, H., Liu, J., and Zheng, S. (2024). "Two-Directional Simultaneous Inference for High-Dimensional Models". Journal of Business & Economic Statistics, 42(1), 298-309.
Lee, S., Seo, M. H., and Shin, Y. (2016). "The Lasso for High Dimensional Regression with a Possible Change Point". Journal of the Royal Statistical Society Series B, 78(1), 193-210.

> Error Structure: exchangeable sequences

Chiang, H. D., Kato, K., and Sasaki, Y. (2023). "Inference for High-Dimensional Exchangeable Arrays". Journal of the American Statistical Association, 118(543), 1595-1605.

b. Linear Quantile Regressions

> Error Structure: iid sequences

Zhang, S., He, X., Tan, K. M., and Zhou, W. X. (2025). "High-Dimensional Expected Shortfall Regression". Journal of the American Statistical Association, 1-12.
Chen, Z., Cheng, V. X., and Liu, X. (2024). "Hypothesis Testing on High Dimensional Quantile Regression". Journal of Econometrics, 238(1), 105525.
Tang, Y., Wang, J-W., and Li, D. (2024). "High-Dimensional Extreme Quantile Regression". Preprint arXiv:2411.13822.
Barendse, S. (2023). "Expected Shortfall LASSO". Preprint arXiv:2307.01033.
Daouia, A., Stupfler, G., and Usseglio-Carleve, A. (2023). "Inference for Extremal Regression with Dependent Heavy-Tailed Data". Annals of Statistics, 51(5), 2040-2066.
He, X., Tan, K. M., and Zhou, W. X. (2023). "Robust Estimation and Inference for Expected Shortfall Regression with Many Regressors". Journal of the Royal Statistical Society Series B, 85(4), 1223-1246.

> Error Structure: exchangeable sequences

Deuber, D., Li, J., Engelke, S., and Maathuis, M. H. (2024). "Estimation and Inference of Extremal Quantile Treatment Effects for Heavy-tailed Distributions". Journal of the American Statistical Association, 119(547), 2206-2216.
Daouia, A., Stupfler, G., and Usseglio-Carleve, A. (2023). "Inference for Extremal Regression with Dependent Heavy-tailed Data". Annals of Statistics, 51(5), 2040-2066.

> Fixed-k Asymptotics with Extreme Value Theory

Daouia, A., Gijbels, I., and Stupfler, G. (2022). "Extremile Regression". Journal of the American Statistical Association, 117(539), 1579-1586.
Sasaki, Y., and Wang, Y. (2022). "Fixed-k Inference for Conditional Extremal Quantiles". Journal of Business & Economic Statistics, 40(2), 829-837.
Müller, U.K., and Wang, Y. (2017). "Fixed-k Asymptotic Inference about Tail Properties". Journal of the American Statistical Association, 112(519), 1334-1343.

Remark 1: Note these results are not to be confused with the fixed-k asymptotics framework commonly used in the nonstationary time series econometrics literature and the high-frequency volatility literature. A major difference is that here we consider inference about tail properties of a distribution based on iid data and extreme value theory. Moreover, related econometric frameworks are also extended to the scenario where a cross-section of data is available for time series observations, although under the maintained assumption of stationary time series.

c. Cross-Sectional Regressions

> Cross-Sectional Estimation and Inference

Wang, H., Liu, B., Feng, L., and Ma, Y. (2023). "Fisher's Combined Probability Test for Cross-Sectional Independence in Panel Data Models with Serial Correlation". Preprint arXiv:2309.08543.
Feng, L., Jiang, T., Liu, B., and Xiong, W. (2022). "Max-Sum Tests for Cross-Sectional Independence of High-Dimensional Panel Data". Annals of Statistics, 50(2), 1124-1143.
Wu, W., Chen, J., Yang, Z., and Tindall, M.L. (2021). "A Cross-Sectional Machine Learning Approach for Hedge Fund Return Prediction and Selection". Management Science, 67(7), 4577-4601.
Fang, Q., Yu, C., and Weiping, Z. (2020). "Regularized Estimation of Precision Matrix for High-Dimensional Multivariate Longitudinal Data". Journal of Multivariate Analysis, 176, 104580.
Chang, J., Chen, S. X., and Chen, X. (2015). "High Dimensional Generalized Empirical Likelihood for Moment Restrictions with Dependent Data". Journal of Econometrics, 185(1), 283-304.
Fan, J., Liao, Y., and Yao, J. (2015). "Power Enhancement in High‐Dimensional Cross‐Sectional Tests". Econometrica, 83(4), 1497-1541.

> GMM Estimation and Factor Models

Lyu, Z., and Yuan, M. (2025). "Large-dimensional Factor Analysis with Weighted PCA". Preprint arXiv:2508.15675.
Chen, Q., Roussanov, N., and Wang, X. (2023). "Semiparametric Conditional Factor Models: Estimation and Inference". NBER Working paper (No. w31817). Available at SSRN 4616885.
Gagliardini, P., and Gouriéroux, C. (2017). "Double Instrumental Variable Estimation of Interaction Models with Big Data". Journal of Econometrics, 201(2), 176-197.
DiTraglia, F. J. (2016). "Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM". Journal of Econometrics, 195(2), 187-208.
Cheng, X., and Liao, Z. (2015). "Select the Valid and Relevant Moments: An Information-based LASSO for GMM with Many Moments". Journal of Econometrics, 186(2), 443-464.

Optional Further Reading

A1. Sample-Splitting Approach for Nearly Nonstationary Time Series

Lui, Y. L., and Ke, S. (2024). "Structural Change Estimator for Models with Episodic Explosiveness and Strongly Dependent Errors". Working paper. Institute for Advanced Economic Research, Dongbei University of Finance and Economics, China.
Katsouris, C. (2023). "Break-Point Date Estimation for Nonstationary Autoregressive and Predictive Regression Models". Preprint arXiv:2308.13915.

A2. Sample-Splitting Approach for High Dimensional Data

> Partial-Sum Asymptotics

Gao, H., Wang, R., and Shao, X. (2025). "Dimension-Agnostic Change Point Detection". Journal of Econometrics (forthcoming).
Enikeeva, F., Klopp, O., and Rousselot, M. (2025). "Change-Point Detection in Low-Rank VAR Processes". Bernoulli, 31(2), 1058-1083.
Li, D., Li, R., and Shang, H. L. (2024). "Detection and Estimation of Structural Breaks in High-Dimensional Functional Time Series". Annals of Statistics, 52(4), 1716-1740.
Horváth, L., and Trapani, L. (2023). "Lp-functionals for Change Point Detection in Random Coefficient Autoregressive Models". Statistics & Probability Letters, 201, 109829.
Wu, T., Volgushev, S., and Shao, X. (2023). "Change-Point Inference for High-Dimensional Heteroscedastic Data". Electronic Journal of Statistics, 17(2), 3893-3941.
Gösmann, J., Stoehr, C., Heiny, J., and Dette, H. (2022). "Sequential Change Point Detection in High Dimensional Time Series". Electronic Journal of Statistics, 16(1), 3608-3671.

> Self-Normalization Approach

Zhang, Z., and Shao, X. (2025). "Hypothesis Testing for a Functional Parameter via Self-Normalization". Journal of the American Statistical Association, (forthcoming).
Zhu, M., Hong, Y., Sun, J., and Linton, O. (2025). "Sequential Change-Point Detection in Time Series: An Adjusted-Range-based Self-Normalization Approach". Working Paper.
Hong, Y., Linton, O., McCabe, B., Sun, J., and Wang, S. (2024). "Kolmogorov–Smirnov Type Testing for Structural Breaks: A New Adjusted-Range based Self-Normalization Approach". Journal of Econometrics, 238(2), 105603.
Cheng, C. H., and Chan, K. W. (2024). "A General Framework for Constructing Locally Self-Normalized Multiple-Change-Point Tests". Journal of Business & Economic Statistics, 42(2), 719-731.
Choi, J. E., and Shin, D. W. (2024). "Subsample Scan Test for Multiple Breaks based on Self-Normalization". Communications in Statistics-Theory and Methods, 53(2), 627-640.
Wang, R., Zhu, C., Volgushev, S., and Shao, X. (2022). "Inference for Change Points in High-Dimensional Data via Self-Normalization". Annals of Statistics, 50(2), 781-806.
Zhang, Y., Wang, R., and Shao, X. (2022). "Adaptive Inference for Change Points in High-Dimensional Data". Journal of the American Statistical Association, 117(540), 1751-1762.
Zhao, Z., Jiang, F., ans Shao, X. (2022). "Segmenting Time Series via Self‐Normalisation". Journal of the Royal Statistical Society Series B, 84(5), 1699-1725.
Choi, J. E., and Shin, D. W. (2021). "A General Panel Break Test based on the Self-Normalization Method". Journal of the Korean Statistical Society, 50(3), 654-680.
Dette, H., Kokot, K., and Volgushev, S. (2020). "Testing Relevant Hypotheses in Functional Time Series via Self-Normalization". Journal of the Royal Statistical Society Series B, 82(3), 629-660.
Wang, R., and Shao, X. (2020). "Hypothesis Testing for High-Dimensional Time Series via Self-Normalization". Annals of Statistics 48(5), 2728-2758.
Pešta, M., and Wendler, M. (2020). "Nuisance-Parameter-free Changepoint Detection in Non-stationary Series". Test, 29(2), 379-408.
Zhang, T., Lavitas, L., and Pan, Q. (2019). "Asymptotic Behavior of Optimal Weighting in Generalized Self‐Normalization for Time Series". Journal of Time Series Analysis, 40(5), 831-851.
Zhang, T., and Lavitas, L. (2018). "Unsupervised Self-Normalized Change-Point Testing for Time Series". Journal of the American Statistical Association, 113(522), 637-648.

A3. Subsampling Approach for Cointegrated Time Series

Remark 2: We briefly discuss related frameworks where the 'subsampling' versus the 'segmented' approaches are used for estimation and inference purposes. Specifically, Politis, Romano & Wolf (2004, JTSA) use the subsampling method applied to properly studentized statistics, which results in confidence intervals and bands with asymptotically correct coverage probability. Moreover, the framework proposed by Demetrescu, Georgiev, Rodrigues & Taylor (2022, JoE) implements the subsampling approach in predictive regression models with persistent predictors. This allows to construct test statistics with desirable theoretical properties for detecting 'episodic predictability' (i.e., periods of statistical significant predictability as defined within the return predictability literature). An interesting aspect worth further research is to construct statistical procedures for testing episodic predictability using self-normalized formulations. Lastly, the studies of Kim (2003, ET), Qu (2007, EJ) and Rodrigues (2024) focus on 'segmented cointegration' testing procedures which rely on the multiple segmentations determination problem. However, testing for Segmented Cointegration for possibly high-dimensional vectors of cointegrated time series data, still remains an open problem in the literature worth investigating further.

Mosaferi, S., Kaiser, M.S., and Nordman, D.J. (2024). "Properties of Test Statistics for Nonparametric Cointegrating Regression Functions Based on Subsamples". Journal of Computational and Graphical Statistics, 33(3), 774-786.
Rodrigues, P.M. (2024). "Persistence Change and Segmented Cointegration Testing". In Oxford Research Encyclopedia of Economics and Finance.
Demetrescu, M., Georgiev, I., Rodrigues, P.M., and Taylor, A.R. (2022). "Testing for Episodic Predictability in Stock Returns". Journal of Econometrics, 227(1), 85-113.
Phillips, P.C.B., Shi, S., and Yu, J. (2014). "Specification Sensitivity in Right‐tailed Unit Root Testing for Explosive Behaviour". Oxford Bulletin of Economics and Statistics, 76(3), 315-333.
Qu, Z. (2007). "Searching for Cointegration in a Dynamic System". The Econometrics Journal, 10(3), 580-604.
Politis, D. N., Romano, J. P., and Wolf, M. (2004). "Inference for Autocorrelations in the Possible Presence of a Unit Root". Journal of Time Series Analysis, 25(2), 251-263.
Kim, J. Y. (2003). "Inference on Segmented Cointegration". Econometric Theory, 19(4), 620-639.
Romano, J. P., and Wolf, M. (2001). "Subsampling Intervals in Autoregressive Models with Linear Time Trend". Econometrica, 69(5), 1283-1314.

A4. Subsampling Approach for High Dimensional Data

Cho, H., Kley, T., and Li, H. (2025). "Detection and Inference of Changes in High-Dimensional Linear Regression with Nonsparse Structures". Journal of the Royal Statistical Society Series B, qkaf029.
Cho, H., and Owens, D. (2024). "High-Dimensional Data Segmentation in Regression Settings Permitting Temporal Dependence and Non-Gaussianity". Electronic Journal of Statistics, 18(1), 2620-2664.
Liu, B., Zhang, X., and Liu, Y. (2024). "Simultaneous Change Point Detection and Identification for High Dimensional Linear Models". Preprint arXiv:2401.08173.
Politis, D. N. (2024). "Scalable Subsampling: Computation, Aggregation and Inference". Biometrika, 111(1), 347-354.
Bai, Y., and Safikhani, A. (2023). "A Unified Framework for Change Point Detection in High-Dimensional Linear Models". Statistica Sinica, 33, 1721-1748.
Wang, H., and Ma, Y. (2021). "Optimal Subsampling for Quantile Regression in Big Data". Biometrika, 108(1), 99-112.
Wang, H., Yang, M., and Stufken, J. (2019). "Information-based Optimal Subdata Selection for Big Data Linear Regression". Journal of the American Statistical Association, 114(525), 393-405.

Related Literature:

Berg, A., McMurry, T. L., and Politis, D. N. (2010). "Subsampling p-values". Statistics & Probability Letters, 80(17-18), 1358-1364.
Politis, D. N., Romano, J. P., and Wolf, M. (1997). "Subsampling for Heteroskedastic Time Series". Journal of Econometrics, 81(2), 281-317.

B1. Testing Serial Correlations in High-Dimensional Time Series

Remark 3: An essential toolkit in the study of high-dimensional statistical methods and machine learning applications is the implementation of concentration inequalities, which provide a mechanism for obtaining non-asymptotic error bounds. However, these probability tools hold under the assumption of sub-Gaussian or sub-Exponential random variables (vectors). Extending to more general exponential type tail assumptions (such as the sub-Weibull), can be useful to certain machine learning applications (such as when using the Lasso in high-dimensional time series). In such high-dimensional environments, with possibly dependent data or weakly dependent data, relevant statistical procedures include testing for the presence of serial correlations as well as testing for mutual independence, which provide evidence regarding their dependence structure.

Tsay, R.S. (2020). "Testing Serial Correlations in High-Dimensional Time Series via Extreme Value Theory". Journal of Econometrics, 216(1), 106-117.
Yao, S., Zhang, X., and Shao, X. (2018). "Testing Mutual Independence in High Dimension via Distance Covariance". Journal of the Royal Statistical Society Series B: Statistical Methodology, 80(3), 455-480.
Lobato, I.N. (2001). "Testing that a Dependent Process is Uncorrelated". Journal of the American Statistical Association, 96(455), 1066-1076.

B2. Testing for Validity of Martingale Difference Hypothesis

Remark 4: A stream of literature focuses on developing statistical procedures for testing the validity of the martingale difference hypothesis (such as testing whether the efficient market hypothesis holds in models for financial economics). From the econometrics point of view, imposing the MDS condition for innovation terms, allows to construct goodness-of-fit tests using model residuals as well as for testing whether under the null hypothesis there is no violation of identification conditions for model parameters, with an econometric specification. Specifically, dynamic econometric models are based on sequences of errors that satisfy the 'unpredictability' condition (although this property is not to be confused with econometric inference for the presence of return predictability using predictive regression models). In general, error terms of time series regression models are assumed to satisfy the serial uncorrelation or white noise property (which implies conditional mean independence). Thus, the MDS condition of error terms can be considered as a model restriction which facilitates the development of asymptotic theory and inference procedures for parameter estimates. Moreover, the MDS condition does not necessarily exclude higher-order dependence, such as when error terms exhibit conditional heteroscedasticity, which in fact for certain econometric specifications the use of time-varying volatility parametrizations ensures valid identification. Therefore, the implementation of such statistical testing procedures with high-dimensional vectors for econometrics and statistics applications can be studied using tools from the high-dimensional statistics literature.

Escanciano, J.C., and Parra, R. (2024). "Extending the Scope of Inference About Predictive Ability to Machine Learning Methods". Preprint arXiv:2402.12838.
Wang, X. (2024). "Generalized Spectral Tests for Multivariate Martingale Difference Hypotheses". Journal of Business & Economic Statistics, 1-27.
Chang, J., Jiang, Q., and Shao, X. (2023). "Testing the Martingale Difference Hypothesis in High Dimension". Journal of Econometrics, 235(2), 972-1000.
Wang, G., Zhu, K., and Shao, X. (2022). "Testing for the Martingale Difference Hypothesis in Multivariate Time Series Models". Journal of Business & Economic Statistics, 40(3), 980-994.
Lee, C.E., and Shao, X. (2018). "Martingale Difference Divergence Matrix and its Application to Dimension Reduction for Stationary Multivariate Time Series". Journal of the American Statistical Association, 113(521), 216-229.
Phillips, P.C.B., and Jin, S. (2014). "Testing the Martingale Hypothesis". Journal of Business & Economic Statistics, 32(4), 537-554.
Clark, T.E., and West, K.D. (2006). "Using Out-of-Sample Mean Squared Prediction Errors to Test the Martingale Difference Hypothesis". Journal of Econometrics, 135(1-2), 155-186.
Escanciano, J.C., and Velasco, C. (2006). "Generalized Spectral Tests for the Martingale Difference Hypothesis". Journal of Econometrics, 134(1), 151-185.

C. Asymptotic Theory Frameworks

Remark 5: The following asymptotic frameworks cover a wide class of econometric environments with different challenges. For example, some of these frameworks require nonparametric procedures which are used to estimate functionals from time series regression models. Specifically, nonparametric (kernel-based) estimation approaches for variance/covariance matrices involve the optimal choice problem of smoothing parameters, such as the bandwidth parameter which is required for consistently estimating the long-run variance of the process. Therefore, these asymptotic frameworks allow to conduct estimation and inference both in finite-samples and in large-samples.

In fact, asymptotic theory expressions for model estimators and test statistics of the various econometric settings aim to produce asymptotically valid inference (asymptotically pivotal). Consider for example, the adaptive estimation approach which can be shown that the same rates of convergence as in an i.i.d setting are achieved. However, there are certain econometric model specifictions and parameter configurations where limit theory discontinuities across the parameter space appears (such as the asymptotic theory for autoregressive parameter in nonstationary autoregressive models), and so the econometrician may decide to focus on constructing estimation procedures for uniform inference across the parameter space (asymptotically equivalent regardless of which region of the parameter space the true parameter falls in), rather than on constructing procedures for maintaining the parametric rate of convergence (robustness-efficiency trade-off).

Another example is the case of fixed-b asymptotics which produces limit results robust to serially dependent error terms, such as when developing estimation and inference procedures for cointegrating regressions. Thus, fixed-b asymptotics allow to obtain serial-dependent and nonstationarity robust inference procedures. For local unit root asymptotics (as in nearly unstable autoregressions and predictive regressions with nearly unstable predictors), to obtain serial-dependent robust inference procedures, researchers proposed to impose an AR structure on the error term rather than just a MDS condition. Then the estimation step can be robustified using a bias correction for estimators of model coefficients and covariance terms (see, Yang et al. (JASA, 2020), Fei, Lui & Yu (2024) and Demetrescu & Rodrigues (2022, JoE)).

Overall, the local to unity asymptotic framework and corresponding limit theory has been employed to develop efficient unit root tests, uniformly valid confidence intervals for parameters of autoregressive models and for the development of robust econometric inference methods for predictive regression models. More recently, the LUR framework, is used to develop test statistics in high-dimensional and data-rich environments such as in the case of Lasso-based estimator in predictive regression models with persistent predictors. Without loss of generality, the main intuition behind these modelling settings, is that the local-to-unity parametrization and the related asymptotic theory results, may provide more accurate approximations of the sampling distributions of the t-statistic in the integrated or nearly integrated settings (such as economic variables which are assumed to predict stock returns and are approximated by nearly integrated processes).

> Fixed-k Asymptotics

Pellatt, D. F., and Sun, Y. (2023). "Asymptotic F test in Regressions with Observations Collected at High Frequency Over Long Span". Journal of Econometrics, 235(2), 1281-1309.
Bollerslev, T., Li, J., and Liao, Z. (2021). "Fixed‐k Inference for Volatility". Quantitative Economics, 12(4), 1053-1084.

> Fixed-b Asymptotics

Casini, A. (2024). "The Fixed-b Limiting Distribution and the ERP of HAR Tests under Nonstationarity". Journal of Econometrics, 238(2), 105625.
Hwang, J., and Valdés, G. (2024). "Low Frequency Cointegrating Regression with Local to Unity Regressors and Unknown Form of Serial Dependence". Journal of Business & Economic Statistics, 42(1), 160-173.
Reichold, K., and Jentsch, C. (2024). "Bootstrap Inference in Cointegrating Regressions: Traditional and Self-Normalized Test Statistics". Journal of Business & Economic Statistics, 42(3), 970-983.
Vogelsang, T.J., and Wagner, M. (2024). "Integrated Modified OLS Estimation and Fixed-b Inference for Cointegrating Multivariate Polynomial Regressions". IHS Working Paper (No. 53). Institute for Advanced Studies, Vienna. Available at https://irihs.ihs.ac.at/id/eprint/6953.
Vogelsang, T.J., and Wagner, M. (2014). "Integrated Modified OLS Estimation and Fixed-b Inference for Cointegrating Regressions". Journal of Econometrics, 178(2), 741-760.
Sun, Y. (2014). "Let’s fix it: Fixed-b Asymptotics versus Small-b Asymptotics in Heteroskedasticity and Autocorrelation Robust Inference". Journal of Econometrics, 178, 659-677.
Sayginsoy, Ö., and Vogelsang, T.J. (2011). "Testing for a Shift in Trend at an Unknown Date: A Fixed-b Analysis of Heteroskedasticity Autocorrelation Robust OLS-based Tests". Econometric Theory, 27(5), 992-1025.
Sun, Y., Phillips, P.C.B., and Jin, S. (2008). "Optimal Bandwidth Selection in Heteroskedasticity–Autocorrelation Robust Testing". Econometrica, 76(1), 175-194.
Bunzel, H. (2006). "Fixed-b Asymptotics in Single-Equation Cointegration Models with Endogenous Regressors". Econometric Theory, 22(4), 743-755.

> In-Fill Asymptotics

Jiang, L., Wang, X., and Yu, J. (2020). "In-Fill Asymptotic Theory for Structural Break Point in Autoregressions". Econometric Reviews, 40(4), 359-386.
Jiang, L., Wang, X., and Yu, J. (2018). "New Distribution Theory for the Estimation of Structural Break Point in Mean". Journal of Econometrics, 205(1), 156-176.

> Local-to-Zero Asymptotics

Wang, W., and Tchatoka, F.D. (2018). "On Bootstrap Inconsistency and Bonferroni-based Size-correction for the subset Anderson–Rubin test under Conditional Homoskedasticity". Journal of Econometrics, 207(1), 188-211.
Phillips, P.C.B., and Gao, W.Y. (2017). "Structural Inference from Reduced Forms with Many Instruments". Journal of Econometrics, 199(2), 96-116.
Caner, M. (2014). "Near Exogeneity and Weak Identification in Generalized Empirical Likelihood Estimators: Many Moment Asymptotics". Journal of Econometrics, 182(2), 247-268.
Hansen, C., and Kozbur, D. (2014). "Instrumental Variables Estimation with Many Weak Instruments using Regularized JIVE". Journal of Econometrics, 182(2), 290-308.
Cattaneo, M.D., Crump, R.K., and Jansson, M. (2012). "Optimal Inference for Instrumental Variables Regression with Non-Gaussian Errors". Journal of Econometrics, 167(1), 1-15.
Li, H., and Xiao, Z. (2012). "Weak Instrument Inference in the Presence of Parameter Instability". The Econometrics Journal, 15(3), 395-419.
Moreira, M.J. (2003). "A Conditional Likelihood Ratio Test for Structural Models". Econometrica, 71(4), 1027-1048.

> Local-to-Unity Asymptotics

Katsouris, C. (2023). "Predictability Tests Robust Against Parameter Instability". Preprint arXiv:2307.15151.
Demetrescu, M., and Rodrigues, P. M. (2022). "Residual-Augmented IVX Predictive Regression". Journal of Econometrics, 227(2), 429-460.
Dou, L., and Müller, U.K. (2021). "Generalized Local‐to‐Unity Models". Econometrica, 89(4), 1825-1854.
Cai, Z., and Wang, Y. (2014). "Testing Predictive Regression Models with Nonstationary Regressors". Journal of Econometrics, 178, 4-14.
Chen, W.W., Deo, R.S., and Yi, Y. (2013). "Uniform Inference in Predictive Regression Models". Journal of Business & Economic Statistics, 31(4), 525-533.
Mikusheva, A. (2012). "One‐Dimensional Inference in Autoregressive Models with the Potential Presence of a Unit Root". Econometrica, 80(1), 173-212.
Mikusheva, A. (2007). "Uniform Inference in Autoregressive Models". Econometrica, 75(5), 1411-1452.
Buchmann, B., and Chan, N.H. (2007). "Asymptotic Theory of Least Squares Estimators for Nearly Unstable Processes under Strong Dependence". Annals of Statistics, 35(5): 2001-2017.
Cavaliere, G., and Taylor, A. R. (2007). "Testing for Unit Roots in Time Series Models with Non-stationary Volatility". Journal of Econometrics, 140(2), 919-947.
Nielsen, B. (2001). "The Asymptotic Distribution of Unit Root Tests of Unstable Autoregressive Processes". Econometrica, 69(1), 211-219.
Cavanagh, C.L., Elliott, G., and Stock, J.H. (1995). "Inference in Models with Nearly Integrated Regressors". Econometric Theory, 11(5), 1131-1147.
Chan, N.H., and Wei, C.Z. (1988). "Limiting Distributions of Least Squares Estimates of Unstable Autoregressive Processes". Annals of Statistics, 367-401.
Phillips, P.C.B., and Perron, P. (1988). "Testing for a Unit Root in Time Series Regression". Biometrika, 75(2), 335-346.
Phillips, P.C.B. (1987). "Towards a Unified Asymptotic Theory for Autoregression". Biometrika, 74(3), 535-547.
Phillips, P.C.B. (1987). "Time Series Regression with a Unit Root". Econometrica, 277-301.

> Drifting Parameter Sequences Asymptotics

Katsouris, C., and Yu, X. (2025). "Improved Uniform Confidence Interval Estimation for Autoregressive Parameter under Nonstationary Volatility". Working paper. Institute of Econometrics and Data Science, Cyprus.
Andrews, D.W., and Li, M. (2024). "Inference in a Stationary/Nonstationary Autoregressive Time-Varying-Parameter Model". Quantitative Economics (forthcoming).
Andrews, D. W., Cheng, X., and Guggenberger, P. (2020). "Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests". Journal of Econometrics, 218(2), 496-531.
Andrews, D.W., and Guggenberger, P. (2014). "A Conditional-Heteroskedasticity-Robust Confidence Interval for the Autoregressive Parameter". Review of Economics and Statistics, 96(2), 376-381.
Andrews, D.W., and Guggenberger, P. (2012). "Asymptotics for LS, GLS, and Feasible GLS Statistics in AR (1) Model with Conditional Heteroskedasticity". Journal of Econometrics, 169(2), 196-210.

> Joint Panel Data Asymptotics

Chetverikov, D., and Manresa, E. (2022). "Spectral and Post-Spectral Estimators for Grouped Panel Data Models". Preprint arXiv:2212.13324.
Phillips, P.C.B. (2018). "Dynamic Panel Anderson-Hsiao Estimation with Roots Near Unity". Econometric Theory, 34(2), 253-276.
Dong, C., Gao, J., and Peng, B. (2015). "Partially Linear Panel Data Models with Cross-Sectional Dependence and Nonstationarity". Available at SSRN 2585334.
Galvao, A.F., and Kato, K. (2014). "Estimation and Inference for Linear Panel Data Models under Misspecification when both N and T are Large". Journal of Business & Economic Statistics, 32(2), 285-309.
Hansen, C.B. (2007). "Asymptotic Properties of a Robust Variance Matrix Estimator for Panel Data when T is Large". Journal of Econometrics, 141(2), 597-620.
Pedroni, P. (2004). "Panel Cointegration: Asymptotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis". Econometric Theory, 20(3), 597-625.
Alvarez, J., and Arellano, M. (2003). "The Time Series and Cross‐Section Asymptotics of Dynamic Panel Data Estimators". Econometrica, 71(4), 1121-1159.
Hahn, J., and Kuersteiner, G. (2002). "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when both N and T are Large". Econometrica, 70(4), 1639-1657.

> Sequential Panel Data Asymptotics

Moral-Benito, E., and Serven, L. (2015). "Testing Weak Exogeneity in Cointegrated Panels". Applied Economics, 47(30), 3216-3228.
Kruiniger, H. (2009). "GMM Estimation and Inference in Dynamic Panel Data Models with Persistent Data". Econometric Theory, 25(5), 1348-1391.
Hadri, K. (2000). "Testing for Stationarity in Heterogeneous Panel Data". The Econometrics Journal, 3(2), 148-161.
Moon, H.R., and Phillips, P.C.B. (2000). "Estimation of Autoregressive Roots Near Unity using Panel Data". Econometric Theory, 16(6), 927-997.
Phillips, P.C.B., and Moon, H.R. (1999). "Linear Regression Limit Theory for Nonstationary Panel Data". Econometrica, 67(5), 1057-1111.

> Diagonal Panel Data Asymptotics

Chao, J.C., and Phillips, P.C.B. (2019). "Uniform Inference in Panel Autoregression". Econometrics, 7(4), 45.
Levin, A., Lin, C.F., and Chu, C.S.J. (2002). "Unit Root Tests in Panel Data: Asymptotic and Finite-Sample Properties". Journal of Econometrics, 108(1), 1-24.

> Fixed Panel Data Asymptotics

Phillips, P. C. B., and Sul, D. (2007). "Bias in Dynamic Panel Estimation with Fixed Effects, Incidental Trends and Cross Section Dependence". Journal of Econometrics, 137(1), 162-188.

> Bootstrap Asymptotics

Wang, Z., Wang, S., and Yan, Y. (2024). "Sieve Bootstrap for Fixed-b Phillips–Perron Unit Root Test". Computational Economics, 64(6), 3181-3205.
Djogbenou, A., Gonçalves, S., and Perron, B. (2015). "Bootstrap Inference in Regressions with Estimated Factors and Serial Correlation". Journal of Time Series Analysis, 36(3), 481-502.
Gonçalves, S., and Perron, B. (2014). "Bootstrapping Factor-Augmented Regression Models". Journal of Econometrics, 182(1), 156-173.
Shao, X., and Politis, D. N. (2013). "Fixed b Subsampling and the Block Bootstrap: Improved Confidence Sets based on p-value Calibration". Journal of the Royal Statistical Society Series B, 75(1), 161-184.
Kreiss, J. P., and Paparoditis, E. (2012). "The Hybrid Wild Bootstrap for Time Series". Journal of the American Statistical Association, 107(499), 1073-1084.
Gonçalves, S. (2011). "The Moving Blocks Bootstrap for Panel Linear Regression Models with Individual Fixed Effects". Econometric Theory, 27(5), 1048-1082.
Chang, Y., Park, J. Y., and Song, K. (2006). "Bootstrapping Cointegrating Regressions". Journal of Econometrics, 133(2), 703-739.
Park, J. Y. (2006). "A Bootstrap Theory for Weakly Integrated Processes". Journal of Econometrics, 133(2), 639-672.
Gonçalves, S., and Kilian, L. (2004). "Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form". Journal of Econometrics, 123(1), 89-120.
Park, J. Y. (2003). "Bootstrap Unit Root Tests". Econometrica, 71(6), 1845-1895.
Paparoditis, E., and Politis, D. N. (2003). "Residual‐based Block Bootstrap for Unit Root Testing". Econometrica, 71(3), 813-855.
Inoue, A., and Kilian, L. (2002). "Bootstrapping Autoregressive Processes with Possible Unit Roots". Econometrica, 70(1), 377-391.

> Limit Experiment Asymptotics

Werker, B. J., and Zhou, B. (2022). "Semiparametric Testing with Highly Persistent Predictors". Journal of Econometrics, 227(2), 347-370.
Müller, U. K., and Norets, A. (2016). "Coverage Inducing Priors in Nonstandard Inference Problems". Journal of the American Statistical Association, 111(515), 1233-1241.
Müller, U.K., and Norets, A. (2016). "Credibility of Confidence Sets in Nonstandard Econometric Problems". Econometrica, 84(6), 2183-2213.
Müller, U.K. (2011). "Efficient Tests Under a Weak Convergence Assumption". Econometrica, 79(2), 395-435.
Jansson, M., and Moreira, M.J. (2006). "Optimal Inference in Regression Models with Nearly Integrated Regressors". Econometrica, 74(3), 681-714.

> Sequentially Randomized Experiments Asymptotics

Kuang, X., and Wager, S. (2024). "Weak Signal Asymptotics for Sequentially Randomized Experiments". Management Science, 70(10), 7024-7041.
Nordin, M., and Schultzberg, M. (2024). "Precision-based Designs for Sequential Randomized Experiments". Preprint arXiv:2405.03487.
Adusumilli, K. (2023). "Optimal Tests following Sequential Experiments". Journal of Political Economy (forthcoming). Preprint arXiv:2305.00403.
Ogbagaber, S. B., Karp, J., and Wahed, A. S. (2016). "Design of Sequentially Randomized Trials for Testing Adaptive Treatment Strategies". Statistics in Medicine, 35(6), 840-858.

> Asymptotics for when Parameters are Near the Boundary of the Parameter Space

Inoue, A., Jordà, Ò, and Kuersteiner, G. M. (2025). "Uniform Validity of the Subset Anderson-Rubin Test under Heteroskedasticity and Nonlinearity". Preprint arXiv:2507.01167.
Cavaliere, G., McCloskey, A., Pedersen, R. S., and Rahbek, A. (2025). "Uniform Critical Values for Likelihood Ratio Tests in Boundary Problems". Preprint arXiv:2507.19603.
Cavaliere, G., Georgiev, I., and Zanelli, E. (2024). "Parameters on the Boundary in Predictive Regression". Preprint arXiv:2409.12611.
Cox, G., and Shi, X. (2023). "Simple Adaptive Size-exact Testing for Full-vector and Subvector Inference in Moment Inequality Models". Review of Economic Studies, 90(1), 201-228.
Elkantassi, S., Bellio, R., Brazzale, A. R., and Davison, A. C. (2023). "Improved Inference for a Boundary Parameter". Canadian Journal of Statistics, 51(3), 780-799.
Fan, Y., and Shi, X. (2023). "Wald, QLR, and Score Tests when Parameters are subject to Linear Inequality Constraints". Journal of Econometrics, 235(2), 2005-2026.
Cavaliere, G., Nielsen, H.B., Pedersen, R.S., and Rahbek, A. (2022). "Bootstrap Inference on the Boundary of the Parameter Space, with Application to Conditional Volatility Models". Journal of Econometrics, 227(1), 241-263.
Cavaliere, G., and Georgiev, I. (2020). "Inference under Random Limit Bootstrap Measures". Econometrica, 88(6), 2547-2574.
Lanne, M., and Luoto, J. (2020). "Identification of Economic Shocks by Inequality Constraints in Bayesian Structural Vector Autoregression". Oxford Bulletin of Economics and Statistics, 82(2), 425-452.
Ketz, P. (2019). "Testing Overidentifying Restrictions with a Restricted Parameter Space". Economics Letters, 185, 108743.
Ketz, P. (2018). "Subvector Inference when the True Parameter Vector may be Near or at the Boundary". Journal of Econometrics, 207(2), 285-306.
Wang, W., and Tchatoka, F. D. (2018). "On bootstrap Inconsistency and Bonferroni-based Size-Correction for the Subset Anderson–Rubin Test under Conditional Homoskedasticity". Journal of Econometrics, 207(1), 188-211.
Cavaliere, G., Nielsen, H. B., and Rahbek, A. (2017). "On the Consistency of Bootstrap Testing for a Parameter On the Boundary of the Parameter Space". Journal of Time Series Analysis, 38(4), 513-534.
McCloskey, A. (2017). "Bonferroni-based Size-correction for Nonstandard Testing Problems". Journal of Econometrics, 200(1), 17-35.
Chen, W. W., and Deo, R. S. (2009). "The Restricted Likelihood Ratio Test at the Boundary in Autoregressive Series". Journal of Time Series Analysis, 30(6), 618-630.
Andrews, D.W. (2001). "Testing when a Parameter is on the Boundary of the Maintained Hypothesis". Econometrica, 69(3), 683-734.
Andrews, D.W. (2000). "Inconsistency of the Bootstrap when a Parameter is on the Boundary of the Parameter Space". Econometrica, 399-405.
Andrews, D.W. (1999). "Estimation when a Parameter is on a Boundary". Econometrica, 67(6), 1341-1383.

> Cube Root Asymptotics

Cattaneo, M. D., Jansson, M., and Nagasawa, K. (2020). "Bootstrap‐based Inference for Cube Root Asymptotics". Econometrica, 88(5), 2203-2219.
Shi, C., Lu, W., and Song, R. (2018). "A Massive Data Framework for M-Estimators with Cubic-Rate". Journal of the American Statistical Association, 113(524), 1698-1709.
Seo, M. H. (2011). "Threshold Autoregression under Misspecification and its Application to Forecasting". Working paper, UCY.

Remark 6: Note that the framework for asymptotics when parameters are near the boundary of the parameter space is suitable for inference when the econometrician imposes inequality restictions on model parameters (see Andrews (1999, 2001 Ecta) and Chen & Deo (2009, JTSA)). Some applications include: Cavaliere, Nielsen & Rahbek (2017, JTSA) who establish the bootstrap consistency when testing whether a parameter is at the boundary, Ketz (2018, JoE) who establish valid inference for subvector testing when a parameter is near the parameter space, and Fan & Shi (2023, JoE) who develop test statistics when parameters are identified using inequality constraints. Recently, Cavaliere, Georgiev & Zanelli (2024, arXiv:2507.19603) develop an inference framework for testing whether inequality constraints are satisfied in the presence of possible nonstationary regressors. Moreover, Cavaliere et al. (2025, arXiv:2507.19603) develop uniform inference for likelihood ratios in boundary problems. Specifically, these authors establish uniform validity for likelihood ratio statistics using a novel approach for constructing critical values that yields uniformly correct asymptotic size, in the presence of nuisance parameters at the boundary of the parameter space. Lastly, asymptotic theory and inference procedures for when parameters are near or at the boundary of the parameter space in high-dimensional settings remains an open problem.

D. Gaussian Approximation Results

Remark 7: Gaussian approximations are useful in statistical inference for time series models. However, establishing Gaussian approximations for non-stationary processes requires different treatment than the case of Gaussian approximations for stationary processes. A first framework towards this direction is given by Bonnerjee, S., Karmakar, S., and Wu, W.B. (AoS, 2024). Moreover, establishing Gaussian approximations for high-dimensional random vectors of non-stationary processes, is currently a new/on-going area of research.

Butucea, C., Meister, A., and Rohde, A. (2025). "Asymptotic Equivalence of Locally Stationary Processes and Bivariate Gaussian White Noise". Annals of Statistics, 53(2), 879-906.
Qiu, J., Chen, S-X., and Shao, Q. (2025). "Self-Normalized Cramer Type Moderate Deviation Theorem for Gaussian Approximation". Annals of Statistics (forthcoming).
Bonnerjee, S., Karmakar, S., and Wu, W.B. (2024). "Gaussian Approximation for Nonstationary Time Series with Optimal Rate and Explicit Construction". Annals of Statistics, 52(5), 2293-2317.
Giessing, A. (2023). "Gaussian and Bootstrap Approximations for Suprema of Empirical Processes". Preprint arXiv:2309.01307.
Deng, H., and Zhang, C-H. (2020). "Beyond Gaussian Approximation: Bootstrap for Maxima of Sums of Independent Random Vectors". Annals of Statistics, 48(6), 3643-3671.
Wang, R., and Shao, X. (2020). "Hypothesis Testing for High-Dimensional Time Series via Self-Normalization". Annals of Statistics, 48(5), 2728–2758.
Koike, Y. (2019). "Gaussian Approximation of Maxima of Wiener Functionals and its Application to High-Frequency Data". Annals of Statistics, 47(3), 1663-1687.
Chernozhukov, V., Chetverikov, D., and Kato, K. (2017). "Central Limit Theorems and Bootstrap in High Dimensions". Annals of Probability, 45(4), 2309-2352.
Zhang, D., and Wu, W.B. (2017). "Gaussian Approximation for High Dimensional Time Series". Annals of Statistics, 45(5), 1895-1919.
Zhang, X., and Cheng, G. (2014). "Bootstrapping High Dimensional Time Series". Preprint arXiv:1406.1037.
Chernozhukov, V., Chetverikov, D., and Kato, K. (2014). "Anti-concentration and Honest, Adaptive Confidence Bands". Annals of Statistics, 42(5), 1787–1818.
Chernozhukov, V., Chetverikov, D., and Kato, K. (2014). "Gaussian Approximation of Suprema of Empirical Processes". Annals of Statistics, 42(4),1564-1597.
Chernozhukov, V., Chetverikov, D., and Kato, K. (2013). "Gaussian Approximations and Multiplier Bootstrap for Maxima of Sums of High-Dimensional Random Vectors". Annals of Statistics, 41(6), 2786-2819.

E. Berry-Esseen Inequality Bounds Results

Kojevnikov, D., and Song, K. (2022). "A Berry–Esseen Bound for Vector-Valued Martingales". Statistics & Probability Letters, 186, 109448.
Kuchibhotla, A.K., Rinaldo, A., and Wasserman, L. (2020). "Berry-Esseen Bounds for Projection Parameters and Partial Correlations with Increasing Dimension". Preprint arXiv:2007.09751.
Zhilova, M. (2020). "Nonclassical Berry–Esseen Inequalities and Accuracy of the Bootstrap". Annals of Statistics, 48(4), 1922-1939.
Jing, B. Y., and Wang, Q. (1999). "An Exponential Nonuniform Berry-Esseen Bound for Self-Normalized Sums". Annals of Probability, 27(4), 2068-2088.
Hall, P., and Jing, B.Y. (1995). "Uniform Coverage Bounds for Confidence Intervals and Berry-Esseen Theorems for Edgeworth Expansion". Annals of Statistics, 23(2), 363-375.

Concluding Remarks

In this module, we aim to discuss in more depth aspects related to the implementation of econometric and machine learning methods for applications in economics as well as when developing estimation and inference approaches in novel environments. Specifically, we give emphasis on the correct use of statistical methods and the implementation of appropriate techniques for the econometric analysis of various data structures.

Generally, when establishing optimal inference procedures for time series regression models, the asymptotics are based on suitable approximations of finite-sample moment functionals with large-sample functionals. In particular, using weak convergence properties for the limit experiments of the model parameter of interest we can derive asymptotic theory which facilitates econometric inference. For example, Jansson, M., and Moreira, M.J. (Ecta, 2006), proposed a framework for optimal inference in predictive regression models based on the local-to-unity parametrization of the autoregressive parameter, where the tests statistics and corresponding limit results hold under the strong assumption of i.i.d. errors. The particular approach can be generalized to predictive regression models in which the error term is a martingale difference sequence with respect to its lags and to current/lagged values of the nearly integrated regressor, but that would be quite challenging. Further studies consider asymptotically valid inference procedures which are robust to the nuisance parameter of persistence, under the assumption of martingale difference sequence errors. The particular approach does have its own challenges that are closely related to the construction of suitable model estimators and test statistics that control for the unknown persistence properties.

All aforementioned asymptotic theory frameworks and the various econometric approaches are governed by 'common statistical laws'. In practice, the main objective of these asymptotic frameworks is to capture the long-run behaviour (at the limit), of the underline equilibria for the stochastic economic models which they correspond to, thereby allowing to conduct statistical/econometric inference. Moreover, when considering implementing different econometric methods, from the theoretical point of view, one needs to establish their asymptotically equivalence under suitable regularity conditions. In addition, insights can be obtained by comparing the performance of competing methods using real and simulated data.

RESEARCH SUPERVISION

During the 2022-2023 academic year, as a Lecturer in Economics in the Department of Economics at the University of Exeter, I also had research supervision responsibilities. I have had the good fortune to advice and learn from the following excellent students.

Undergraduate research supervision:

Davin Young (BS.c. (Hons) in Financial Economics, Graduated July 2023). BSc Dissertation Title: "Econometric Analysis of Cross-Sectional Data with LASSO Regression".

> This undergraduate dissertation was motivated by our interest in understanding whether a factor-augmented model is on average better in terms of out-of-sample forecast accuracy than a simple, possibly autoregressive model. The idea was to compare the performance of conventional EPA tests to that of JYP (ET, 2023) for the above settings as well as when a shrinkage estimator for the cross-section is employed.

Sam Hartshorn (BS.c. (Hons) in Economics, Graduated July 2023). BSc Dissertation Title: "Conventional and Unconventional Monetary Policy in the United Kingdom".

Postgraduate research supervision:

Jiayang Li (MS.c. in Financial Economics, Graduated December 2023). MSc Dissertation Title: "The Evolution of Banking Sector in Europe" (International Finance).

> This postgraduate dissertation was motivated by our interest in understanding and modelling systemic risk and financial contagion in the European banking sector. We employ a dynamic panel data model and based on a novel panel dataset consisting of a set of firm-specific and macroeconomic variables, we model the determinants of NPL loans across main European economics such as Germany and France. We use synthetic data simulations to examine the presence of systemic risk heterogeneities.

Yiming Zhao (MS.c. in Financial Economics, Graduated December 2023). MSc Dissertation Title: "Forecast Evaluation under the presence of Instabilities" (Applied Time Series Econometrics).
Hang Du (MS.c. in Financial Economics, Graduated December 2023). MSc Dissertation Title: "Macroeconomic Shocks in Difference-in-Difference Models during the Pandemic" (Applied Macroeconometrics).
Impana Bharadwaj (MS.c. in Financial Economics, Graduated December 2023). MSc Dissertation Title: "Firm Performance and Green Investing" (Financial Economics).

TEACHING EXPERIENCE

University of Southampton, United Kingdom

Graduate Teaching Assistant (2018-2021)

Department of Economics

ECON 3015: Principles of Finance (Undergraduate), Fall 2018, 2019, 2020
- Responsibilities: Master classes, office hours, grading & feedback.
ECON 2026: Introduction to Econometrics (Undergraduate), Fall 2019
- Responsibilities: Stata workshop, Master classes, office hours, grading & feedback.

Department of Social Statistics and Demography

STAT 3010: Statistical Methods in Insurance (Undergraduate), Spring 2021
- Responsibilities: R workshop and problem sets tutorials, office hours (online).
STAT 6093: Survey Fundamentals (Graduate), Fall 2020
- Responsibilities: Stata workshops and problem sets tutorials, office hours (online).

Prior teaching activities

University of Cyprus, Cyprus

Teaching Assistant (2015 - 2017)

ECO 222: Introduction to Econometrics (Undergraduate), Fall 2015
- Responsibilities: Stata and problem sets tutorials, office hours, grading, exam invigilation.
Econometrics & Statistics Casual Demonstrator, Spring 2016, Fall 2016, Spring 2017, Fall 2017

Main modules covered: ECO222, ECO223, MAS051, MAS102, MAS121.
Responsibilities: Q&As, explanation of module material.

University of Bath, United Kingdom

Mathematics Drop-in Demonstrator (2010 - 2011)

Mathematics Resource Centre (MASH), Department of Mathematical Sciences

Private Education, Cyprus

Mathematics and Statistics Teacher (2012-2014, Summer 2015, Fall 2017)

As a Mathematics & Statistics teacher, (pre-PhD), I gained additional teaching experience by organising and preparing revision classes ('surgery' sessions) for mainly undergraduate students on courses such as

Linear Algebra, Probability Theory, Statistical Distribution and Inference Theory
Applied Statistics, Mathematical Methods for PDEs, Multivariate Calculus
Business Economics, Quantitative Methods in Economics

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