题目：Testing for Series Correlation and ARCH Effect of High-Dimensional Time Series Data
报告人：凌仕卿  香港科技大学教授
报告时间：2019年7月26日（周五）下午13：30
地点：国际经管学院315会议室（诚明楼三层）
主办方：国际经济管理学院

摘要：This paper proposes several tests for detecting serial correlation and ARCHeffect in high-dimensional data. The dimension of data p = p(n) may go toinfinity when the sample size n → ∞. It is shown that the sample autocorrela-tion function and the sample rank autocorrelation function (Spearman’s rank correlation) of the L 1 −norm of data are asymptotically normal, respectively. Two portmanteau tests respectively based on the norm and its rank are shown to be asymptotically χ 2 -distributed, and the corresponding weighted portmanteau tests are shown to be asymptotically distributed as a linear combination of independent χ 2 random variables. These tests are dimension-free,i.e. independent of p, and the norm rank-based portmanteau test and the corresponding weighted portmanteau test can be used for heavy-tailed time series. Two standardized norm-based tests are further discussed. Simulation results show that these test statistics have satisfactory sizes and are very powerful even for small n and large p. Two real data examples are given.