Matrix-valued Factor Model with Time-varying Main Effects

TL;DR

This paper introduces the MEFM, a flexible matrix-valued model with time-varying effects, providing estimators, tests, and demonstrating its effectiveness on NYC Taxi data.

Contribution

It generalizes traditional matrix factor models to include time-varying effects, with rigorous estimation, testing procedures, and real data application.

Findings

MEFM outperforms traditional FM in simulations.

The proposed test effectively detects the need for MEFM.

Application to NYC Taxi data shows MEFM's advantages.

Abstract

We introduce the matrix-valued time-varying Main Effects Factor Model (MEFM). MEFM is a generalization to the traditional matrix-valued factor model (FM). We give rigorous definitions of MEFM and its identifications, and propose estimators for the time-varying grand mean, row and column main effects, and the row and column factor loading matrices for the common component. Rates of convergence for different estimators are spelt out, with asymptotic normality shown. The core rank estimator for the common component is also proposed, with consistency of the estimators presented. We propose a test for testing if FM is sufficient against the alternative that MEFM is necessary, and demonstrate the power of such a test in various simulation settings. We also demonstrate numerically the accuracy of our estimators in extended simulation experiments. A set of NYC Taxi traffic data is analysed and our test suggests that MEFM is indeed necessary for analysing the data against a traditional FM.