报告题目：Optimal Inference and Forecasting in High-Dimensional Time Series using Dense Linear Regression Models
报告人：何易
阿姆斯特丹大学
报告时间：2024年10月8日(周二) 16:30-18:00
报告地点：中国科学院数学与系统科学研究院南楼N204
腾讯会议ID：107 694 240
内容摘要
Most high-dimensional economic data exhibit dense relationships that cannot be effectively captured by sparse models. In the dense world of big data, traditional empirical weighting strategies fail because the covariance structure among many variables cannot be consistently recovered. Using random matrix theory, we analytically derive the asymptotic limits of the power of quadratic tests and the mean squared estimation errors of Tikhonov estimators across various weighting strategies. The optimal solution turns out to be the simplest: apply equal weighting in hypothesis testing and use ridge regression for forecasting, with an equally weighted penalty. Notably, unlike Lasso regression, ridge regression is robust to the factor structure in economic data without requiring special adjustments. This challenges the conventional wisdom in econometric analysis, which often emphasizes complex weight optimizations, and explains why simpler methods frequently outperform more sophisticated ones in real-world big data applications. Further analysis reveals that high-dimensional quadratic tests typically require size correction when dealing with time series data, while the standard k-fold cross-validation used to find the optimal ridge penalty for i.i.d. data also applies correctly to time series data.
主讲人简介
Yi He is an Associate Professor in the Quantitative Economic Section at the University of Amsterdam. He earned his master’s degree from the University of Cambridge and his PhD from Tilburg University in 2016. Prior to returning to the Netherlands, he served as a tenured Assistant Professor in the Department of Econometrics and Business Statistics at Monash University in Australia. His research focuses on high-dimensional econometrics, random matrix theory, extreme value statistics, bootstrapping, and machine learning. His work has been featured in prestigious journals, including the Journal of the American Statistical Association, The Annals of Statistics, Journal of the Royal Statistical Society - Series B, Journal of Business & Economic Statistics, and Journal of Econometrics. Yi's breakthroughs in extreme value statistics have earned him a nomination for the 2025 Van Dantzig Award in Statistics and Operations Research in the Netherlands. His current research explores dense time series models with complex network interactions in high-dimensional econometrics.
