Threshold Tensor Factor Model in CP Form

TL;DR

This paper introduces a Threshold Tensor Factor Model in CP form that captures regime-switching dynamics in tensor time series, providing a parsimonious and interpretable approach with proven estimation properties.

Contribution

The paper develops a novel threshold tensor factor model in CP form with estimation procedures and theoretical guarantees, addressing regime-switching in tensor time series.

Findings

Model effectively captures regime changes in tensor data

Estimation procedures have desirable theoretical properties

Numerical and real-data experiments demonstrate practical utility

Abstract

This paper proposes a new Threshold Tensor Factor Model in Canonical Polyadic (CP) form for tensor time series. By integrating a thresholding autoregressive structure for the latent factor process into the tensor factor model in CP form, the model captures regime-switching dynamics in the latent factor processes while retaining the parsimony and interpretability of low-rank tensor representations. We develop estimation procedures for the model and establish the theoretical properties of the resulting estimators. Numerical experiments and a real-data application illustrate the practical performance and usefulness of the proposed framework.