FACTOR MODELLING FOR HIGH-DIMENSIONAL TIME SERIES: INFERENCE AND MODEL SELECTION

Analysis of high-dimensional time series data is of increasing interest among different fields. This article studies high-dimensional time series from a dimension reduction perspective using factor modelling. Statistical inference is conducted using eigen-analysis of a certain non-negative definite matrix related to autocovariance matrices of the time series, which is applicable to fixed or increasing dimension. When the dimension goes to infinity, the rate of convergence and limiting distributions of estimated factors are established. Using the limiting distributions of estimated factors, a high-dimensional final prediction error criterion is proposed to select the number of factors. Asymptotic properties of the criterion are illustrated by simulation studies and real applications.