Threshold factor models for high-dimensional time series

Abstract We consider a threshold factor model for high-dimensional time series in which the dynamics of the time series is assumed to switch between different regimes according to the value of a threshold variable. This is an extension of threshold modeling to a high-dimensional time series setting under a factor structure. Specifically, within each threshold regime, the time series is assumed to follow a factor model. The regime switching mechanism creates structural changes in the factor loading matrices. It provides flexibility in dealing with situations that the underlying states may be changing over time, as often observed in economic time series and other applications. We develop the procedures for the estimation of the loading spaces, the number of factors and the threshold value, as well as the identification of the threshold variable, which governs the regime change mechanism. The theoretical properties are investigated. Simulated and real data examples are presented to illustrate the performance of the proposed method.