High Dimensional Covariance Matrix Estimation Using a Factor Model
2006/12/12
研討會日期 : 2006-12-12
時間 : 15:00
主講人 : Prof. Jianqing Fan
地點 : B棟110會議室
演講者簡介 : Prof. Jianqing Fan為Ph. D., University of California at Berkeley。
現為Frederick L. Moore '18 Professor of Finance, Princeton University。
其主要研究領域為Financial Economics, Risk Management, Bioinformatics, Data-analytic modeling, Nonlinear time series, Analysis of longitudinal data, Model selections, Nonparametric inferences, Wavelets, Survival Analysis, Generalized linear models, Mathematical statistics。
演講摘要 : Large dimensionality comparable to the sample size is a common feature as in modern portfolio allocation and risk management. In this paper we examine the covariance matrix estimation in the asymptotic framework that the dimensionality p grows with sample size. Motivated by the Capital Asset Pricing Model, we propose to use a multi-factor model to reduce the dimensionality and to estimate the covariance matrix among those assets. Under some basic assumptions, we have established the rate of convergence and asymptotic normality for the proposed covariance matrix estimator.
The performance is compared with the sample covariance matrix. We identify the situations under which the factor approach can gain substantially the performance and the cases where the gains are only marginal. Furthermore, the impacts of the covariance matrix estimation on portfolio allocation and risk management are studied respectively. The asymptotic results are supported by a thorough simulation study.
