Estimation of latent factors for high-dimensional time series

Abstract

This paper deals with the dimension reduction of high-dimensional time series based on common factors. In particular we allow the dimension of time series p to be as large as, or even larger than, the sample size n. The estimation of the factor loading matrix and the factor process itself is carried out via an eigenanalysis of a p p non-negative definite matrix. We show that when all the factors are strong in the sense that the norm of each column in the factor loading matrix is of the order p 1/2 , the estimator of the factor loading matrix is weakly consistent in L 2 -norm with the convergence rate independent of p. This result exhibits clearly that the 'curse' is canceled out by the 'blessing' of dimensionality. We also establish the asymptotic properties of the estimation when factors are not strong. The proposed method together with their asymptotic properties are further illustrated in a simulation study. An application to an implied volatility data set, together with a trading strategy derived from the fitted factor model, is also reported.