Robust Statistical Inference for Large-dimensional Matrix-valued Time Series via Iterative Huber Regression

TL;DR

This paper develops robust statistical inference methods for large-dimensional matrix-valued time series using iterative Huber regression, effectively handling heavy-tailed errors and diverging dimensions.

Contribution

It introduces a robust estimation framework with convergence rates, asymptotic distributions, and consistent rank estimation for matrix factor models in high dimensions.

Findings

Iterative Huber regression is practical and reliable for heavy-tailed data.

Proposed methods perform well in real financial and macroeconomic datasets.

The estimators achieve desirable convergence and asymptotic properties.

Abstract

Matrix factor model is drawing growing attention for simultaneous two-way dimension reduction of well-structured matrix-valued observations. This paper focuses on robust statistical inference for matrix factor model in the ``diverging dimension" regime. We derive the convergence rates of the robust estimators for loadings, factors and common components under finite second moment assumption of the idiosyncratic errors. In addition, the asymptotic distributions of the estimators are also derived under mild conditions. We propose a rank minimization and an eigenvalue-ratio method to estimate the pair of factor numbers consistently. Numerical studies confirm the iterative Huber regression algorithm is a practical and reliable approach for the estimation of matrix factor model, especially under the cases with heavy-tailed idiosyncratic errors . We illustrate the practical usefulness of the proposed methods by two real datasets, one on financial portfolios and one on the macroeconomic indices of China.