Factor analysis for high-dimensional time series: Consistent estimation and efficient computation

To deal with the factor analysis for high-dimensional stationary time series, this paper suggests a novel method that integrates three ideas. First, based on the eigenvalues of a non-negative definite matrix, we propose a new approach for consistently determining the number of factors. The proposed method is computationally efficient with a single step procedure, especially when both weak and strong factors exist in the factor model. Second, a fresh measurement of the difference between the factor loading matrix and its estimate is recommended to overcome the nonidentifiability of the loading matrix due to any geometric rotation. The asymptotic results of our proposed method are also studied under this measurement, which enjoys "blessing of dimensionality." Finally, with the estimated factors, the latent vector autoregressive (VAR) model is analyzed such that the convergence rate of the estimated coefficients is as fast as when the samples of VAR model are observed. In support of our results on consistency and computational efficiency, the finite sample performance of the proposed method is examined by simulations and the analysis of one real data example.