High-Dimensional Covariance Matrices under Dynamic Volatility Models: Asymptotics and Shrinkage Estimation
Prof. Yi DING
Assistant Professor in Business Intelligence and Analytics
FBA, UM
Date: 16 January 2024 (Tuesday)
Time: 1:00pm to 2:00pm
Venue: FBA Lobby
Abstract
We study the estimation of high-dimensional covariance matrices and their empirical spectral distributions under dynamic volatility models. Data under such models have nonlinear dependency both cross-sectionally and temporally. We establish the condition under which the limiting spectral dis-tribution (LSD) of the sample covariance matrix under scalar BEKK models is different from the i.i.d. case. We then propose a time-variation adjusted (TV-adj) sample covariance matrix and prove that its LSD follows the Marˇcenko-Pastur law. Based on the asymptotics of the TV-adj sample covariance matrix, we develop a consistent population spectrum estimator and an asymptotically optimal nonlinear shrinkage estimator of the unconditional covariance matrix.
Speaker
Dr. Ding is an Assistant Professor of Business Intelligence Analytics at the Faculty of Business Administration in University of Macau. She received her Ph.D.degree in Business Statistics from the Hong Kong University of Science and Technology and the Bachelor ofScience degree in Mathematics and Applied Mathematics from Tsinghua University. Before joining University of Macau, Dr. Ding worked as a Research Assistant Professor in the Department of Applied Mathematics at Hong Kong Polytechnic University. Her research focuses on the study of financial big data, financial econometrics, and high-dimensional statistics. Dr. Ding has published papers in top academic journals such as Journal of the American Statistical Association and Journal of Econometrics. She has been the principal investigator of research projects funded by the Hong Kong Research Grant Council, and the National Natural Science Foundation of China.
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