Premium
Factor Modelling for High‐Dimensional Time Series: Inference and Model Selection
Author(s) -
Chan Ngai Hang,
Lu Ye,
Yau Chun Yip
Publication year - 2017
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12207
Subject(s) - mathematics , autocovariance , series (stratigraphy) , dimension (graph theory) , inference , statistical inference , factor analysis , dimensionality reduction , model selection , time series , selection (genetic algorithm) , asymptotic distribution , statistics , computer science , mathematical analysis , artificial intelligence , paleontology , fourier transform , estimator , biology , pure mathematics
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.