Dimension Reduction in Multivariate Time Series

Abstract

This article compares models for dimension reduction in time series and tests of the dimension of the dynamic structure. We consider both stationary and nonstationary time series and discusses canonical analysis, prin- cipal components, scalar components models, reduced rank models and factor models. The unifying view of canonical correlation analysis between the present and past values of the series is emphasized. We review some of the tests based on canonical correlation analysis to Þnd the dimension of the dynamic relation- ship among the time series, and we propose a new test to Þnd the number of common factors. The test is based on the common eigenstructure of the gen- eralized covariance matrices of the process and its performance is illustrated through Monte Carlo simulations.