Statistical inference for large-dimensional tensor factor model by iterative projections

TL;DR

This paper introduces a projection estimator for tensor factor models that improves convergence rates and employs an iterative eigenvalue-ratio method for determining factor numbers, with extensive numerical validation.

Contribution

It proposes a novel projection estimator for Tucker-decomposition tensor factor models with faster convergence and a new iterative method for factor number determination.

Findings

Projection estimator has faster convergence than PCA-based methods.

The iterative eigenvalue-ratio procedure accurately determines factor numbers.

Numerical studies show superior empirical performance of the proposed methods.

Abstract

Tensor Factor Models (TFM) are appealing dimension reduction tools for high-order large-dimensional tensor time series, and have wide applications in economics, finance and medical imaging. In this paper, we propose a projection estimator for the Tucker-decomposition based TFM, and provide its least-square interpretation which parallels to the least-square interpretation of the Principal Component Analysis (PCA) for the vector factor model. The projection technique simultaneously reduces the dimensionality of the signal component and the magnitudes of the idiosyncratic component tensor, thus leading to an increase of the signal-to-noise ratio. We derive a convergence rate of the projection estimator of the loadings and the common factor tensor which are faster than that of the naive PCA-based estimator. Our results are obtained under mild conditions which allow the idiosyncratic components to be weakly cross- and auto- correlated. We also provide a novel iterative procedure based on the eigenvalue-ratio principle to determine the factor numbers. Extensive numerical studies are conducted to investigate the empirical performance of the proposed projection estimators relative to the state-of-the-art ones.