时 间：2020年12月14日（周一）10:00-11:00
地 点：理科大楼A1716（中山北路校区）
题 目: On testing high dimensional white noise
主讲人：李曾 南方科技大学助理教授
摘 要：
Testing for white noise is a classical yet important problem in statistics, especially for diagnostic checks in time series modeling and linear regression. For high-dimensional time series in the sense that the dimension p is large in relation to the sample size T, the popular omnibus tests including the multivariate Hosking and Li–McLeod tests are extremely conservative, leading to substantial power loss. To develop more relevant tests for high-dimensional cases, we propose a portmanteau-type test statistic which is the sum of squared singular values of the first qq lagged sample autocovariance matrices. It, therefore, encapsulates all the serial correlations (up to the time lag q) within and across all component series. Using the tools from random matrix theory and assuming both p and Tdiverge to infinity, we derive the asymptotic normality of the test statistic under both the null and a specific VMA(1) alternative hypothesis. As the actual implementation of the test requires the knowledge of three characteristic constants of the population cross-sectional covariance matrix and the value of the fourth moment of the standardized innovations, nontrivial estimations are proposed for these parameters and their integration leads to a practically usable test. Extensive simulation confirms the excellent finite-sample performance of the new test with accurate size and satisfactory power for a large range of finite (p,T) combinations, therefore, ensuring wide applicability in practice. In particular, the new tests are consistently superior to the traditional Hosking and Li–McLeod tests.
报告人简介：
李曾，南方科技大学统计与数据科学系助理教授。2017年获得香港大学统计与精算学系博士学位，2017-2019年先后在美国华盛顿大学、宾夕法尼亚州立大学从事博士后研究工作，并于2019年入职南方科技大学。主要研究领域为随机矩阵理论、高维统计分析等，研究成果发表于The Annals of Statistics, Scandinavian Journal of Statistics 等国际统计学期刊。