Estimation of latent factors for high-dimensional time series

This paper deals with the dimension reduction of high-dimensional time series based on a lower-dimensional factor process. In particular, we allow the dimension of time series N to be as large as, or even larger than, the length of observed time series T. The estimation of the factor loading matrix and the factor process itself is carried out via an eigenanalysis of a N×N 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 N-super-1/2, the estimator of the factor loading matrix is weakly consistent in L 2 -norm with the convergence rate independent of N. Thus the curse is cancelled out by the blessing of dimensionality. We also establish the asymptotic properties of the estimators when factors are not strong. The proposed method together with the asymptotic properties are illustrated in a simulation study. An application to an implied volatility data set, with a trading strategy derived from the fitted factor model, is also reported. Copyright 2011, Oxford University Press.