Adaptive Estimation for Non-stationary Factor Models And A Test for Static Factor Loadings

TL;DR

This paper develops adaptive estimation and testing methods for non-stationary factor models with time-varying loadings, allowing for high-dimensional data and local stationarity, with validation through simulations and real data.

Contribution

It introduces a novel adaptive sieve estimator for the loading space and a bootstrap-assisted test for static loadings in locally stationary factor models.

Findings

Estimator is uniformly consistent in simulations.

Test effectively distinguishes static from dynamic loadings.

Methods perform well under high-dimensional settings.

Abstract

This paper considers the estimation and testing of a class of locally stationary time series factor models with evolutionary temporal dynamics. In particular, the entries and the dimension of the factor loading matrix are allowed to vary with time while the factors and the idiosyncratic noise components are locally stationary. We propose an adaptive sieve estimator for the span of the varying loading matrix and the locally stationary factor processes. A uniformly consistent estimator of the effective number of factors is investigated via eigenanalysis of a non-negative definite time-varying matrix. A possibly high-dimensional bootstrap-assisted test for the hypothesis of static factor loadings is proposed by comparing the kernels of the covariance matrices of the whole time series with their local counterparts. We examine our estimator and test via simulation studies and real data analysis. Finally, all our results hold at the following popular but distinct assumptions: (a) the white noise idiosyncratic errors with either fixed or diverging dimension, and (b) the correlated idiosyncratic errors with diverging dimension.