- "Portfolio Analysis in High Dimensions with Tracking Error and Weight Constraints"(with M. Fan-CUHK) Accepted November 2025, Forthcoming- at Journal of the American Statistical Association(JASA). Theory and Methods. arXiv-Mehmet Caner: https://arxiv.org/abs/2402.17523v2 (you will be directed via link). Contact author. https://doi.org/10.1080/01621459.2025.2602832 January 5 2026, dated latest article in JASA.
The paper provides a data dependent way of solving and estimating stochastic inequality constraints for tracking error and weight formation in a large portfolio. This is a new finding in large portfolio formation. We can show high dimensional consistency of weight estimates, variance and the Sharpe Ratio even when the number of assets is larger than the sample size. Rate of convergence results are derived both for unconstrained and constrained portfolios. There is extensive analysis of tracking error, joint tracking error and weight constraints, only weight constraints, both equality and inequality constraints are hendled. We also provide a data dependent way of understanding whether weight constraints are binding or not too. There is no analysis of a general short selling constraint in this paper.
"A practitioner's guide to AI+ML Portfolio Investing" Invited Article-Econometric Reviews (2026), with M. Fan, CUHK. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5546200. Vol 45-issue 7, 876-911, lead article in that issue.
The paper analyzes certain methods in quantitative investing based on precision matrix and is used in real investing. Some of these ideas are currently used by hedge funds. We analyze sevreal time periods in US markets especially downturns.
"Deep Learning Based Residuals in Non-linear Factor Models:
Precision Matrix Estimation of Returns with Low Signal-to-Noise Ratio" joint with Maurizio Daniele (ETH-Zurich).Accepted 2025 August, Journal Of Econometrics (251), 106083. September 2025 issue. We provide online appendix with more proofs.
A sparse deep learning estimator with proofs are here in Supplement. All the code-data are with Maurizio Daniele-ETH Zurich.
The paper develops a novel deep learning based thresholded covariance matrix estimator. Then via a novel matrix inversion formula, estimates the precision matrix. We assume covariance matrix of nonlinear unknown factors is singular. Shows also with larger number of assets deep learning based covariance matrix of errors reach min-max optimal bound, results in strong empirical performance. This estimator can estimate unknown nonlinear relation and perform at least as good as linear models.
4."Should Humans Lie to Machines? The Incentive Compatibility of Lasso and Generalized Linear Models Structured Sparsity Estimators" Joint with Kfir Eliaz (Tel Aviv Univ.) 2024, vol.42, p.1379-1388, Journal of Business and Economic Statistics.
In this article we show that even the machines are good intentioned, humans may have an incentive to lie, if only statistical algorithms are used. With the added economic incentive compatibility criterion, this issue may be resolved. Incentive compatibility between machines and humans will be essential for the future. The paper is trying to open a new avenue for research combining game theory with high dimensional econometrics. Here are the proofs and some sims. Supplement.
5. "Generalized Linear Models with Structured Sparsity Estimators" Accepted 2023, Single authored article. 2023, Journal of Econometrics, 236(2), October 2023 Issue.
In this article, I propose a new nonlinear machine learning technique. The loss is based on generalized linear models and if we know the structure of the sparsity in our model we can get confidence intervals (uniform-honest-valid) for our structural parameters. Estimators are based on GLM loss with general structured penalty.This results in better power of the tests against an unstructured sparsity type of penalty function. I also provide new oracle inequalities with weaker norm when the penalty of the estimator is in stronger norm. Also a uniformity argument is proved for the paremeters in nonlinear loss functions. A feasible weighted nodewise regression is introduced with new oracle inequality to solve singularity issues in sample second order partial derivative matrix of nonlinear loss function.
Main part of the paper in the journal will have the main oracle inequality proof.
The supplement has simulations: Supplement Appendix. The nodewise regression proofs with CLT proof and the uniformity proof is in Online Appendix (also refereed, but since its long it will show up here only). We also have a tuning parameter choice theorem in this online appendix.
6. "Sharpe-Ratio Analysis in High Dimensions: Residual-Based Nodewise Regression in Factor Models" with M. Medeiros(PUC-Rio), G.Vasconcelos(PUC-Rio). 2023, Journal of Econometrics, vol.235(2), 393-417.August 2023 issue.
In this paper we propose a novel way of merging machine learning-big data-artificial intelligence and factor models. We propose a residual based nodewise regression in factor models to estimate the precision matrix of errors and use this in precision matrix of returns. We allow number of assets to exceed the time span of the portfolio. Hence we use these new precision matrix estimators to get consistency of maximum Sharpe Ratio estimate. Also maximum out of sample Sharpe Ratio consistency is achieved, and mean-variance efficiency of portfolio is established. Simulations and empirical evidence show that this new method works well compared to shrinkage and pure factor model based methods. This can be used as a new financial product in the financial industry for large portfolio formation.
7." A nodewise regression approach to estimating large portfolios" with L. Callot(Amazon), O. Onder(Ege Univ), E. Ulasan(Ege Univ.). 2021 J. of Business and Economics Statistics, 39,520-531.
In this paper, we develop a new way of estimating the variance, the risk, and the weights of global minimum variance and Markowitz mean-variance portfolios even when the number of stocks are more than the time span of the portfolio. It uses concept of nodewise regression which is a machine learning technique. We provide both consistency and the rate of convergence of our estimator. Nodewise regression delivers better results than the factor models, linear shrinkage method in certain scenarios in an out of sample forecasting exrecise. Here are the proofs: Appendix
8. "An upper bound for functions of estimators in high dimensions" with X Han(City Univ. Hong Kong), 2021, Econometric Reviews,vol40-1, 1-13.
We provide an alternative to delta theorem in high dimensions. The key to rate of convergence of estimators is the dimension and behavior
of the gradient, which was not a factor in fixed dimensions.
9. "Partners in debt: An endogenous non-linear analysis of the effects of public and private debt on growth".(with Q.Fan-Chinese Univ of Hong Kong, T. Grennes), 2021, International Review of Economics and Finance", 76, 694-711.
We apply a new threshold analysis on public-private debt interaction, and we find that is the key to understanding growth empirically. Household debt plays also an important role.
10. "A starting note: A historical perspective in lasso" International Econometric Review, 2021, 13, p1-3.
11. "Inference in partially identified models with many moment inequalities using lasso" with F. Bugni, A.B. Kock, S. Lahiri, Journal of Statistical Planning and Inference. 2020, 206, 211-248.
In this paper, we show that with high number of moment inequalities, a two step process is helpful in testing the underlying parameter of interest. By thresholding with lasso we show we can select binding moments well, and then feed them into second stage to get inference with better power.
12. "Asymptotically Honest Confidence Regions for High Dimensional Parameters by the Desparsified Conservative Lasso" with Anders B Kock (Oxford-Aarhus), 2018, J. of Econometrics, 203, 143-168.
In this paper we provide a simple closed form estimator which works even when the number of parameters exceed number of observations. This can be thought as extending least squares to high dimensions. We provide
heteroskedascity consistent standard errors, confidence intervals, and inference in large number of coefficients. At this point our code can be obtained from Anders B Kock.
We recommend conservative lasso based estimator coupled with BIC for applied economists. Closed form estimator is in equation (9) in the second equality. Here is an R code, for 1 of Tables with no correlation: desplasso2.R
13. "Adaptive Elastic Net GMM Estimation with Many Invalid Moment Conditions: Simultaneous Model and Moment Selection" with X. Han (City Univ Hong Kong), Y. Lee (Syracuse). 2018. J. of Business and Economics Statistics,36, 24-46.
In the paper we propose a new estimator that can simultaneously estimate the structural parameters without using invalid moments even though there may be invalid moments. If we have locally invalid moments, we use them to get estimates and get an more efficient result. The code: please consult Xu Han. For a sample dynamic panel data code: dpanel1.R
14."Sharp Threshold Detection Based on Sup-norm Error Rates in High Dimensional Models" with L. Callot, (Free Univ. Amsterdam), A.B. Kock (Arhus Uni), and J.A. Riquelme, 2017, 35, 250-264. J. of Business and Economics Statistics.
In the paper we develop a new estimator for structural coefficients in a threshod model in hi dimensional framework. We are able to show in which variables regime shift occurs, also simultaneously we see whether there is a regime shift. In this sense, it gets rid of two step former process of testing for threshold and then estimating the model.
15.“Determining the number of factors with potentially strong block correlation error
terms” Econometric Reviews, 2017, 36, 946-969.(main author: Xu Han, Caner
Contribution is very very minor).
Paper is availaible from Xu Han.
16. An oracle inequality for Convex Models " with A. Bredahl Kock , Arhus. Econometric Reviews, 2016, 35, 1377-1411.
This is an article that proves an oracle inequality for elastic net in a general convex loss function. This generalizes Buhlmann and Van de Geer , 2011 book result of convex loss with lasso to elastic net.
17."Moment and IV selection approaches: A Comparative Simulation Study". with Essie Maasoumi, J. Andres Riquelme, Econometric Reviews,2016, 35, 1562-1581.
A simulation study that analyzes moment selection approaches in an IV framework, also looks at large number of moments case. Adaptive lasso based technique does well generally. The computer programs can be obtained from jariquel@ncsu.edu. (Juan Andres Riquelme)
18."Hybrid GEL Estimators: Instrument Selection with Adaptive Lasso", with Michael Fan, Xiamen University, WISE, Journal of Econometrics.July 2015, 187, 256-274.
This paper analyzes GEL estimators after selecting the instruments through adaptive lasso. Has favorable finite sample properties, please see M Fan for code:qfan@ncsu.edu. or michaelqfan@gmail.com.
19."Near Exogeneity and Weak Identification in Generalized Empirical Likelihood Estimators: Many Moment Asymptotics", 2014, Journal of Econometrics, vol. 18, Issue 2, p.247-268.
This article analyzes tests in a general violation of exogeneity setting in combination with many weak moments in generalized empirical likelihood estimators. The interesting result is both the mean and variance for estimators change due to this violation. We have new limits for estimators and tests depending on the magnitude of the violation as well as the number of moments. A gauss code for TABLE 4B for Anderson-Rubin test is provided: arnem and R Version of the same program: arnem.R
20."Selecting the Correct Number of Factors in Approximate Factor Models: The Large Panel Case with Group Bridge Estimator" 2014, Journal of Business and Economics Statistics, with Xu Han, City University of Hong Kong, vol.32, issue 3, 359-374.
For code please consult Xu Han. The paper provides a novel way of selecting number of factors thru factor loading penalization. On the way it introduces a new group bridge shrinkage estimator.
21."Adaptive Elastic Net GMM with Diverging Number of Moments", 2014 , vol.32, p30-47, Journal of Business and Economics Statistics, joint with Helen Zhang, Math Department, University of Arizona. Gauss code for simulations in the text aenet2.
R code aenetgmm.Rwho does limited simulations, but some initial value problems in optimizer, please run several times. The paper shows adaptive elastic net with diverging number of moments, but does only model selection with diverging number of parameters, no moment selection in this paper.
22. "Valid Tests When Instrumental Variables Do Not Perfectly Satisfy the Exclusion Restriction" 2013, Stata Journal, , Andres Riquelme, Dan Berkowitz,. This is STATA function for paper "The Validity of Instruments Revisited" J. of Econometrics, 2012,below. Shows a resampling technique that is robust to minor violations of exogeneity, and uses data dependent critical values for Anderson-Rubin test. It contains a better function than paper 6, and has extensive simulations in the paper, and empirical example.
23. "An Alternative to Unit Root Tests: Bridge Estimators Differentiate between Nonstationary versus Stationary Models and Select Optimal Lag", 2013, 143, 691-715 Journal of Statistical Planning and Inference, with Keith Knight, University of Toronto,
Department of Statistics. The paper proposes Bridge estimators to select nonstationary versus stationary models.
A gauss program that we used in simulations, Table 1b, Setup1, Design 1: ubridgebics1, and an R program that shows how to implement this with simulated data: urbbic.R
24. "CUE with nearly-singular design and many weak moment asymptotics". 2012, Journal of Econometrics,170, p.422-441, with N. Yildiz, Rochester .
The paper finds what happens when there are highly correlated instruments in a many weak asymptotics framework.
A computer program for simulations in Table 2, in Gauss: jkgmm1
25. "The Validity of Instruments Revisited", 2012, Journal Of Econometrics,(with Dan Berkowitz,Univ. of Pittsburgh,Ying Fang, Xiamen Univ.) Vol.166-2, 255-267.
This paper calculates a resampled Anderson-Rubin test that is also robust to local violations of exogeneity in instruments.
Gauss Files:sbcfrh(calculates Table 12, row 3, in our paper), far (shows how to do this with controls), t7a(an application with table7a dataset from Acemoglu-Johnson-Robinson,AER, 2001)
Stata files:far.ado is a function, and here is the help file: far.pdf and Table7a.dta is from Acemoglu-Johnson-Robinson,AER, 2001. You can load your own data and use this program, just you have to enter variable names.
26. "Editor's Introduction, Thirty years of GMM", 2012, Journal of Econometrics, (with Marine Carrasco (main editor), Yuichi Kitamura, Eric Renault)166-2, 251-255.
27. "Pivotal Structural Change Tests in Linear Simultaneous Equations Models with Weak Identification", 2011 Econometric Theory. Vol 27.2. 413-427.
28."A Pretest to Differentiate Between Weak and Nearly-Weak Instrument Asymptotics", 2011, International Econometric Review.
29."Determinants of Norwegian Sovereign Wealth Fund Shares: Lucas Paradox Survives", with Turanay Caner, Tom Grennes.2011, Global Economy Journal, Berkeley Electronic Press.
30. "Exponential Tilting with Weak Instruments: Estimation and Testing", 2010, Oxford Bulletin of Economics and Statistics.72, 307-326.
31. "Sovereign Wealth Funds: the Norwegian Experience" with Tom Grennes, The World Economy, 2010, 33, 597-614.
32. "Testing, Estimation in GMM and CUE with Nearly-Weak Identification", Econometric Reviews, 2010, 29, 330-363 .
33.Book Chapter: "Finding The Tipping Point-When Sovereign Debt Turns Bad" Sovereign Debt and Financial Crisis ,(refereed), 2010, (joint with Tom Grennes,NCSU, Fritzi Koehler-Geib, World Bank),p64-75.
34. "The Norwegian Sovereign Wealth Fund" (joint with Tom Grennes,NCSU). Revue d'Economie Financiere, 2009.(Invited Article)
35. "LASSO Type GMM Estimator" Econometric Theory, 2009, 25, 1-23.
36. "Nearly-Singular Design in GMM and Generalized Empirical Likelihood Estimators" Journal of Econometrics, 2008, 144, 511-523.
37."Are Nearly Exogenous Instruments Reliable?" with D. Berkowitz, Y. Fang, Economics Letters, 2008, 101, 20-23.
38. "Boundedly Pivotal Structural Change Tests in Continuous Updating GMM with Strong, Weak Identification and Completely Unidentified Cases" Journal of Econometrics, 2007, 137, 28-67.
39. " M Estimators with Non-Standard Rates of Convergence and Weakly Dependent Data", April 2006, Journal of Statistical Planning and Inference, 136, 1207-1219.
40. Corrigendum with E. Basci, G. Yoon on "Are real exchange rates nonstationary or non-linear? Evidence from a new threshold unit root test". Studies in Nonlinear Dynamics and Econometrics, 2006, March.
41. "Are Real Exchange Rates non-stationary or non-linear? Evidence from a new Threshold Unit Root Test," (with E. Basci, Central Bank of Turkey ). Studies in Nonlinear Dynamics and Econometrics, 2005,vol. 9.4.
42. " Instrumental Variable Estimation of a Threshold Model," ( with Bruce Hansen, University of Wisconsin-Madison), Econometric Theory, vol.20, October 2004. p.813-843.
43. "Time-Varying Betas Help in Asset Pricing: Threshold CAPM," ( with L. Akdeniz and A. Salih, Bilkent University). Studies in Nonlinear Dynamics and Econometrics 2003, January.
44." A Note on LAD Estimation of a Threshold Model," Econometric Theory, 18, June 2002, 800-814. (Appeared in Articles Section)
45." Threshold Autoregressions with a Unit Root," ( with Bruce E. Hansen), Econometrica,69, November 2001, 1555-1597.
46. " Size Distortions of Tests of the Null Hypothesis of Stationarity: Evidence and Implications for the PPP debate," (with Lutz Kilian, Univ. of Michigan), Journal of International Money and Finance, 20, October 2001, 639-657.
47. "Tests for Cointegration with Infinite Variance Errors," Journal of Econometrics, 86, September 1998,155-175.
48. "A Locally Optimal Seasonal Unit Root Test," Journal of Business and Economic Statistics, 16, July 1998, 349-356.
49. "Weak Convergence to a Matrix Stochastic Integral with Stable Processes," Econometric Theory, 13, August 1997,506-29.