Estimation of Constrained Factor Models for High‐Dimensional Time Series

ABSTRACT This article studies the estimation of the constrained factor models for high‐dimensional time series. The approach is based on the eigenanalysis of a nonnegative definite matrix constructed from the autocovariance matrices. The convergence rate of the estimator for loading matrix and the asymptotic normality of the estimated factor score are explored under regularity conditions set for the proposed model. Our estimation for the constrained factor models can achieve the optimal rate of convergence even in the case of weak factors. The finite sample performance of our approach is examined and compared with the existing methods by Monte Carlo simulations. Our methodology is illustrated and supported by a real data example.