Projected Estimation for Large-dimensional Matrix Factor Models

TL;DR

This paper introduces a projection estimation method for large-dimensional matrix factor models that enhances factor analysis by reducing noise and improving convergence rates, with applications in finance and macroeconomics.

Contribution

The study proposes a novel projection-based estimation technique that simplifies analysis and achieves faster convergence for large matrix factor models with cross-sectional spikes.

Findings

Projection method reduces noise and improves signal-to-noise ratio.

Projected estimators have faster convergence rates than existing methods.

Numerical and real data studies confirm the method's effectiveness.

Abstract

In this study, we propose a projection estimation method for large-dimensional matrix factor models with cross-sectionally spiked eigenvalues. By projecting the observation matrix onto the row or column factor space, we simplify factor analysis for matrix series to that for a lower-dimensional tensor. This method also reduces the magnitudes of the idiosyncratic error components, thereby increasing the signal-to-noise ratio, because the projection matrix linearly filters the idiosyncratic error matrix. We theoretically prove that the projected estimators of the factor loading matrices achieve faster convergence rates than existing estimators under similar conditions. Asymptotic distributions of the projected estimators are also presented. A novel iterative procedure is given to specify the pair of row and column factor numbers. Extensive numerical studies verify the empirical performance of the projection method. Two real examples in finance and macroeconomics reveal factor patterns across rows and columns, which coincides with financial, economic, or geographical interpretations.