Identification and estimation for matrix time series CP-factor models

TL;DR

This paper introduces a novel method for identifying and estimating CP-factor models in matrix time series that offers faster convergence and handles rank-deficient matrices, outperforming previous eigenanalysis-based approaches.

Contribution

The paper presents a new joint diagonalization approach that improves convergence rates and accommodates rank-deficient matrices in CP-factor model estimation.

Findings

Faster convergence rates independent of eigengaps.

Ability to handle rank-deficient factor loading matrices.

Validated effectiveness on simulated and real data.

Abstract

We propose a new method for identifying and estimating the CP-factor models for matrix time series. Unlike the generalized eigenanalysis-based method of Chang et al. (2023) for which the convergence rates of the associated estimators may suffer from small eigengaps as the asymptotic theory is based on some matrix perturbation analysis, the proposed new method enjoys faster convergence rates which are free from any eigengaps. It achieves this by turning the problem into a joint diagonalization of several matrices whose elements are determined by a basis of a linear system, and by choosing the basis carefully to avoid near co-linearity (see Proposition 5 and Section 4.3). Furthermore, unlike Chang et al. (2023) which requires the two factor loading matrices to be full-ranked, the proposed new method can handle rank-deficient factor loading matrices. Illustration with both simulated and real matrix time series data shows the advantages of the proposed new method.