Econometric Methods for Risk Assessment and Forecasting
So.Fi.E. Summer School
June 16-20 2025, Brussels, Belgium
June 16-20 2025, Brussels, Belgium
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The upcoming SoFiE Summer School offers an in-depth exploration of cutting-edge econometric methods, with a focus on time series density forecasting, vector autoregressions (VARs), and factor models. This comprehensive program is divided into three specialized modules, each led by a renowned expert in the field. Participants will gain both theoretical knowledge and practical experience, with real-world applications in sectors such as energy and finance.
This intensive program offers participants the opportunity to engage with leading academics, develop practical skills through hands-on applications, and expand their network within the econometrics community. Whether you’re an academic, researcher, or industry professional, this summer school provides cutting-edge tools for advancing your expertise in time series forecasting and econometric modeling.
The audience includes graduate students, academics, practitioners, and policymakers. Apply here.
Instructors
Francesco Ravazzolo is Full Professor of Econometrics at Faculty of Economics and Management at Free University of Bozen-Bolzano and Head of the Department of Data Science and Analytics at BI Norwegian Business School. He is also co-founder of AIAQUA and COMMODIA. His research focuses on commodity markets, data anlytics, econometrics, energy economics, financial econometrics and macroeconometrics. He has published in several leading academic journals. Francesco serves the academia in several roles. He is in the editorial board of the following journals: Annals of Applied Statistics; International Journal of Forecasting; Journal of Applied Econometrics; Spatial Economic Analysis; Studies in Nonlinear Dynamics and Econometrics. He is president of the Society of Nonlinear Dynamics and Econometrics.
Francesca Loria is a CEPR research affiliate in the Monetary Economics and Fluctuations (MEF) programme, serves as an associate editor for the Journal of Money, Credit and Banking, and is a principal economist at the Federal Reserve Board. She specializes in time series econometrics and macro-economic risk. Her research has been published in leading journals, including the Journal of Monetary Economics, the Review of Economics and Statistics, The Economic Journal, and the Journal of Economic Literature. She has co-taught advanced modeling and macroeconometric methods to economists in academia, central banks, government agencies, and the private sector. Francesca developed statistical toolboxes for macroeconomic forecasting (F.I.T.) and for evaluating quantitative business cycle models (BCAppIt!).
Dimitris Korobilis is a Professor of Econometrics at the Adam Smith Business School, University of Glasgow. His research focuses on time series analysis, macroeconomic and financial forecasting, and high-dimensional inference, using Bayesian statistics and machine learning. He has developed econometric models for central banks and policy institutions. He is also an adjunct researcher at CAMP (BI Norwegian Business School), a senior fellow at RCEA, and a board member of ESOBE. Additionally, he serves as an associate editor for the Journal of Business and Economic Statistics and Studies in Nonlinear Dynamics and Econometrics. In 2020, he founded the MSc in Data Analytics for Economics and Finance at Glasgow. Previously, he held roles at the University of Essex and CORE at Université Catholique de Louvain.
Program
Program
Time Series Density Forecasting and Combination
Francesco Ravazzolo
Density Forecasting
Reduced Form VARs: Introduction to Vector Autoregressions (VARs) and their application in modeling multivariate time series data.
Density Forecasting with VARs: Exploration of both Bayesian and frequentist approaches to generate density forecasts using VAR models.
Evaluation of Forecasts: Techniques for assessing the accuracy and reliability of density forecasts.
Applications: Participants will engage in practical applications, with a focus on sectors such as energy, to solidify their understanding.
Density Forecast Combinations
Bayesian Model Averaging: Study of methods to combine forecasts from multiple models using Bayesian principles.
Extension to Time-Varying Combination Weights and Learning: Investigation into dynamic weighting schemes that adapt over time for improved forecast combinations.
Combinations of Large Data Sets: Strategies for handling and integrating extensive datasets in forecast combinations.
Applications: Practical application exercises, potentially within the energy sector, to apply theoretical concepts.
Structural Vector Autoregressions
Francesca Loria
Constant-parameter Structural VARs: Analysis of VAR models that incorporate structural information to identify causal relationships.
Regime-Switching Parameter Structural VARs: Examination of VAR models that account for regime changes in time series data.
Proxy Structural VARs: VAR Models that use external instruments to identify and estimate the effects of structural shocks in economic time series data.
Applications:
Policy Impacts: Identifying causal effects of monetary policy shocks on the macroeconomy using SVARs and proxy SVARs.
Outlook-at-Risk: Assessment of the potential downside risks to economic growth using MS-VAR techniques.
Beyond the Mean: Predictors & Factor Models for Distributional Analysis
Dimitris Korobilis
Quantile Regression and Quantile Factor Models: Regressions and factor models for characterizing individual quantiles of a variable of interest.
Tail Index Regression: Methods for modeling and forecasting extreme values in financial and economic data.
Bayesian Density Regression: Flexible parameteric and nonparametric methods that allow covariates to affect the whole distribution of a dependent variable rather than just its mean.
Applications:
Quantile Factor Augmented Vector Autoregression (QFAVAR): Structural Inference and Forecasting: Utilization of QFAVAR models for structural analysis and predictive purposes.
A Tail Risk Index: Development of a Tail Index factor model to monitor tail risks in stock markets.
Key references
Time Series Density Forecasting and Combination
Francesco Ravazzolo
Aastveit, K.A., J. Mitchell, F. Ravazzolo and H.K. van Dijk, (2018). The Evolution of Forecast Density Combinations in Economics, Oxford Research Encyclopedia of Economics and Finance
Bassetti, F, R. Casarin and F. Ravazzolo, (2020). Density Forecasting. In Fuleky, P. (eds) Macroeconomic Forecasting in the Era of Big Data, Springer.
Bassetti, F., Casarin, R., Ravazzolo, F. (2018). Bayesian Nonparametric Calibration and Combination of Predictive Distributions, Journal of the American Statistical Association, 113(522), 675-685.
Billio, Casarin, Ravazzolo and van Dijk, (2013). Time-varying Combinations of Predictive Densities using Nonlinear Filtering, Journal of Econometrics, 177(2), 213–232.
Casarin, Grassi, Ravazzolo and van Dijk, (2015). Parallel Sequential Monte Carlo for Efficient Density Combination: The Deco Matlab Toolbox, Journal of Statistical Software, 68(3).
Casarin, R, S. Grassi, F. Ravazzolo and H.K. van Dijk (2023), “A Flexible Predictive Density Combination for Large Financial Data Sets in Regular and Crisis Periods”. Journal of Econometrics, 237(2), 105370.
Catania, L., S. Grassi and F. Ravazzolo, (2019). Forecasting Cryptocurrencies under Model and Parameter Instability. International Journal of Forecasting, 39(2), 485-501.
Clark and Ravazzolo, (2015). The Macroeconomic Forecasting Performance of Autoregressive Models with Alternative Specifications of Time-Varying Volatility, Journal of Applied Econometrics, 30(4), 551-575.
Del Negro, M. and Schorfheide, F. (2010). Bayesian Macroeconometrics, Handbook of Bayesian Econometrics.
Gianfreda, A., F. Ravazzolo and L. Rossini (2020). “Comparing the Forecasting Performances of Linear Models for Electricity Prices with High-RES Penetration”. International Journal of Forecasting, 36(3), 974-986.
Gianfreda, A., F. Ravazzolo and L. Rossini (2023), “Large Time-Varying Volatility Models for Electricity Prices”. Oxford Bulletin of Economics and Statistics, 85(3), 545-573.
Iacopini, M., F. Ravazzolo and L. Rossini (2023), “Proper Scoring Rules for Evaluating Asymmetry in Density Forecasting”. Journal of Business and Economic Statistics, 2, 482-496.
Lerch, S., T. Thorarinsdottir, F. Ravazzolo and T. Gneiting, (2017). Forecaster's Dilemma: Extreme Events and Forecast Evaluation. Statistical Science, 32(1), 106-127.
Litterman, R. B., (1986). Forecasting with Bayesian vector autoregressions five years of experience. Journal of Business and Economic Statistics, (4):25-38.
Koop, G. (2003). Bayesian Econometrics, J. Wiley.
Ravazzolo, F. and L. Rossini (2025), “Is the Price Cap for Gas Useful? Evidence from European Countries”. Annals of Applied Statistics, forthcoming.
West, M., and J. Harrison, (1997). Bayesian Forecasting and Dynamic Models, 2nd Ed., Springer
Structural Vector Autoregressions
Francesca Loria
Key readings:
Andrle, M. and Plasil, M. (2018). "Econometrics with System Priors". Economics Letters, 172, 134–137.
Baumeister, C. and Hamilton, J. D. (2015): "Sign Restrictions, Structural Vector Autoregressions, and Useful Prior Information," Econometrica, 83, 1963–1999.
Caldara, D., Cascaldi-Garcia, D., Cuba Borda, P. and Loria, F. (2025). "Understanding Growth-at-Risk: A Markov-Switching Approach." Mimeo.
Caldara, D. and E. Herbst (2019): "Monetary Policy, Real Activity, and Credit Spreads: Evidence from Bayesian Proxy SVARs," American Economic Journal: Macroeconomics, 11, 157–192.
Hamilton, J. D. (1989). "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle." Econometrica, 57 (2), 357–384.
Other useful references:
Tobias Adrian, Nina Boyarchenko, Francesco Furno, Domenico Giannone, Leonardo Iania, Michele Lenza, Francesca Loria, Cecilia Melo Fernandes, Sergio Sola (2025). "Macro Risk." Mimeo.
Baumeister, C., Maih, J. and Loria, F. (2025). "Flexible Priors and Restrictions for Structural Vector Autoregressions." Mimeo.
Baumeister, C. and Hamilton, J. D. (2018). "Inference in Structural Vector Autoregressions When the Identifying Assumptions are Not Fully Believed: Re-evaluating the Role of Monetary Policy in Economic Fluctuations". Journal of Monetary Economics, 100 (C), 48–65.
Baumeister, C. and Hamilton, J. D. (2019). "Structural Interpretation of Vector Autoregressions with Incomplete Identification: Revisiting the Role of Oil Supply and Demand Shocks". American Economic Review, 109 (5), 1873–1910.
Binning, A. and Maih, J. (2015). "Applying Flexible Parameter Restrictions in Markov-Switching Vector Autoregression Models." Working Papers No 12/2015, Centre for Applied Macro- and Petroleum Economics (CAMP), BI Norwegian Business School.
Diebold, F. X., Lee, J.-H., and Weinbach, G. C. (1994). "Regime Switching with Time-Varying Transition Probabilities". In Granger, C. W. J. and Newbold, P. (eds.), Nonstationary Time Series Analysis and Cointegration. Oxford University Press.
Filardo, A. J. (1994). "Business-Cycle Phases and Their Transitional Dynamics". Journal of Business & Economic Statistics, 12 (3), 299–308.
Sims, C. A. and Zha, T. (1998). "Bayesian Methods for Dynamic Multivariate Models." International Economic Review, 39 (4), 949–968.
Beyond the Mean: Predictors & Factor Models for Distributional Analysis
Dimitris Korobilis
Key readings:
Adrian, T., Boyarchenko, N., and Giannone, D. (2019). Vulnerable Growth. American Economic Review, 109(4), 12631289.
Korobilis, D. and Schroeder, M. (2025). Monitoring Multi-Country Macroeconomic Risk: A Quantile Factor-Augmented Vector Autoregressive (QFAVAR) Approach, Journal of Econometrics, 249, 105730.
Korobilis, D. and Schroeder, M. (forthcoming). Probabilistic Quantile Factor Analysis, Journal of Business and Economic Statistics.
Nicolau, J., Rodrigues, P. M. M. and Stoykov, M. Z. (2023). Tail index estimation in the presence of covariates: Stock returns’ tail risk dynamics, Journal of Econometrics 235(2), 2266-2284.
Nicolau, J. and Rodrigues, P. M. M. (2024). A simple but powerful tail index regression. Working Paper.
Korobilis, D., Mamatzakis, E. and Pappas, V. (2024). “Bayesian Nonparametric Inference in Bank Business Models with Transient and Persistent Cost Inefficiency”
Other useful references
Plagborg-Møller, M., Reichlin, L., Ricco, G. and Hasenzagl, T. (2020) When is growth at risk?, Brookings Papers on Economic Activity.
Beirlant, J., Vynckier, P., & Teugels, J. L. (1996). Tail index estimation, Pareto quantile plots, and regression diagnostics. JASA, 91, 1659-1667.
Beirlant, J., Goegebeur, Y. (2003). Regression with response distributions of Pareto-type. Computational Statistics & Data Analysis, 42, 595-619.
Csörgõ, S., Deheuvels, P., & Mason, D. (1985). Kernel estimates of the tail index of a distribution. Ann. Statist., 13, 1050-1077.
Dekkers, A. L. M., Einmahl, J. H. J., & de Haan, L. (1989). A moment estimator for the index of an extreme value distribution. Ann. Statist., 17, 1833-1855.
Hill, B. M. (1975). A simple general approach to inference about the tail of a distribution. Ann. Statist., 3, 1163-1174.
Wang, H., & Tsai, C.-L. (2009). Tail index regression. JASA, 104(487), 1233-1240.
Kelly, B. T., Pruitt, S. and Su, Y. (2019) Characteristics are covariances: A unified model of risk and return, Journal of Financial Economics, 134(3), 501-524.
Kelly, B. T., Pruitt, S. and Su, Y. (2020) Instrumented Principal Component Analysis, working paper, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2983919.
Barro, R. J. (2006). Rare disasters and asset markets in the twentieth century. Quarterly Journal of Economics, 121(3):823–866.
Bollerslev, T. and Todorov, V. (2011). Tails, fears, and risk premia. Journal of Finance, 66(6):2165–2211.
Kelly, B. and Jiang, H. (2014). Tail risk and asset prices. Review of Financial Studies, 27(10):2841–2871.
Ang, A., Chen, J., and Xing, Y. (2006). Downside risk. Review of Financial Studies, 19(4):1191–1239.
Chavez-Demoulin, V. and Davison, A. C. (2005). Generalized additive models for sample extremes. Journal of the Royal Statistical Society: Series C, 54(1):207–222.
Tokdar, S. T., Jiang, S., and Cunningham, E. L. (2024). Heavy-tailed density estimation. Journal of the American Statistical Association, 119(545):163–175.
Dunson, D. B., Pillai, N. and Park, J-H. (2007) Bayesian density regression, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 69(2), 163-183.
Rigon, T. and Durante, D. (2021) Tractable Bayesian density regression via logit stick-breaking priors, Journal of Statistical Planning and Inference, 211, 131142.
How to participate?
How to participate?
To participate, please complete the registration form and submit your application to Prof. Leonardo Iania at leonardo.iania@uclouvain.be by the 10th of May, with the words “SoFiE Summer School 2025" in the subject box. Decisions will be emailed out by the 15th of May 2025. The applications should include a CV and, in the text of the email, a brief motivation on why you would like to attend this course. The course will offer a limited number of course participants an opportunity to present their current research and receive feedback from the instructors and other course participants. Students interested in making a presentation (which is optional, on a competitive basis and not guaranteed) should indicate so on their application and submit a draft of the research paper that they wish to promote.
Fees: 400 Euro for (full-time) Ph.D. students, 600 for (full time) academics (Post-docs, Profs, etc.) and 1100 Euro for others. All accepted participants are expected to be members of the Society for Financial Econometrics or to join before their place is confirmed. The course is free for full-time Ph.D. students from Belgian Universities (conditional on acceptance). Further info on how to join SoFiE is available at https://www.stern.nyu.edu/experience-stern/about/departments-centers-initiatives/centers-of-research/volatility-and-risk-institute/sofie (where a student membership option is available). Fees cover the inscription costs, lunches, and coffee breaks foreseen in the program. Confirmation of admission of selected applicants is conditional on receipt of the fee payment in due time (details to be provided in the admission email).
Venue
Venue
Auditorium of the National Bank of Belgium
Montagne aux Herbes Potagères, 61 1000 Brussels.
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Organizing institutions
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