Projected Estimation for Large-dimensional Matrix Factor Models

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.

arXiv commentThis is a revised version of the original paper "Two-stage Projected Estimation for Large-dimensional Matrix Factor Models"

References in corpus (4)

• Factor modeling for high-dimensional time series: Inference for the number of factors
• Independent component analysis for tensor-valued data
• Sparse latent factor models with interactions: Analysis of gene expression data
• Learning Latent Factors from Diversified Projections and its Applications to Over-Estimated and Weak Factors