INFERENCE ON THE MAXIMAL RANK OF TIME-VARYING COVARIANCE MATRICES USING HIGH-FREQUENCY DATA

• 成果类型: Article
• 署名作者: Reiss, Markus; Winkelmann, Lars
• 署名单位: Humboldt University of Berlin; Free University of Berlin
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2273
• 发表日期: 2023
• 页码: 791-815
• 关键词: volatility; dimension; number

摘要

We study the rank of the instantaneous or spot covariance matrix ⠂X (t) of a multidimensional process X (t). Given high-frequency observations X(i/n), i = 0, ... , n, we test the null hypothesis rank(⠂X(t)) & LE; r for all t against local alternatives where the average (r + 1)st eigenvalue is larger than some signal detection rate vn. A major problem is that the inherent averaging in local covariance statistics produces a bias that distorts the rank statistics. We show that the bias depends on the regularity and spectral gap of ⠂X(t). We establish explicit matrix perturbation and concentration results that provide nonasymptotic uniform critical values and optimal signal detection rates vn. This leads to a rank estimation method via sequential testing. For a class of stochastic volatility models, we determine data-driven critical values via normed p-variations of estimated local covariance matrices. The methods are illustrated by simulations and an application to high-frequency data of U.S. government bonds.