Identifying the number of factors from singular values of a large sample auto-covariance matrix.

Abstract

This paper first proposes a complete theory for singular values of lagged sample autocovariance matrices from a high-dimensional factor model covering both the factor part and the noise part assuming that the dimension and the sample size proportionally grow to infinity. In particular, we provide an exact description of the phase transition phenomenon that determines whether a factor is strong enough to be detected asymptotically. Next, we propose a new and strongly consistent estimator for the number of significant factors including both weak and pervasive factors. In all tested cases, the new estimator largely outperforms existing estimators using the same ratios of singular values.