Identification and estimation of threshold matrix‐variate factor models

Abstract

Motivated by the growing availability of complex time series observed in real applications, we propose a threshold matrix‐variate factor model, which simultaneously addresses the sample‐wise and time‐wise complexities of a time series. The sample‐wise complexity is characterized by modeling matrix‐variate observations directly, while the time‐wise complexity is modeled by a threshold variable to describe the nonlinearity in time series. The estimators for loading spaces and threshold values are introduced and their asymptotic properties are investigated. Our matrix‐variate models compress data more efficiently than traditional vectorization‐based models. Furthermore, we greatly extend the scope of current research on threshold factor models by removing several restrictive assumptions, including existence of only one threshold, fixed factor dimensions across different regimes, and stationarity within regime. Under the relaxed assumptions, the proposed estimators are consistent even when the numbers of factors are overestimated. Simulated and real examples are presented to illustrate the proposed methods.

Core Content Selection and Textbook Design for High School Mathematics

“…The matrix factor model was further extended to the constrained version by Chen et al (2020). Additional extensions include the threshold matrix factor model studied by Liu and Chen (2022). Furthermore, Chen et al (2023) investigated a time-varying matrix factor model allowing for smooth changes in the factor loading matrices over time.…”