Shrinkage estimation of multiple threshold factor models

Abstract

This paper proposes a multiple threshold factor model to enhance the flexibility in modeling the underlying regime switching mechanism for high dimensional time series. The factor loadings are assumed to switch between different regimes according to the value of a threshold variable. A novel estimation procedure is proposed to consistently estimate the multiple thresholds with the aid of sorting operation, principal component analysis and shrinkage estimation, which is practically easy-to-implement and computationally efficient. Furthermore, asymptotic properties for the multiple threshold estimators are established, together with other theoretical results. Monte Carlo simulations demonstrate that the procedure works well in finite samples. The U.S. data sets are analyzed with the proposed model to illustrate the threshold effect of economy policy uncertainty on the financial market.