Inference for time-varying factor models under local stationarity

Abstract

This paper considers estimation of and testing for a class of locally stationary time series factor models with evolutionary dynamics, where the entries and dimension of the factor loading matrix are allowed to vary with time while the factors and idiosyncratic components are locally stationary. We propose an adaptive sieve estimator for the span of the time-varying loading matrix of a locally stationary factor process. A uniformly consistent estimator of the effective number of factors is developed via eigenanalysis of a non-negative definite time-varying matrix. We also propose a possibly high-dimensional bootstrap test for the hypothesis of constant factor loadings by comparing the kernels of the covariance matrices of the whole time series with their local counterparts. This test avoids the assumption that factors and idiosyncratic errors are stationary or the covariance matrix of factors is time-invariant. Our results cover both cases of white noise idiosyncratic errors and serially correlated idiosyncratic errors. We examine the finite sample performance of our proposed estimator and test via simulation studies and real data analysis.