Likelihood inferences for high dimensional factor analysis of time series with applications in finance

This paper investigates likelihood inferences for high-dimensional factor analysis of time series data. A matrix decomposition technique is developed to obtain expressions of the likelihood functions and its derivatives. With such expressions, the traditional delta method that relies heavily on score function and Hessian matrix can be extended to high dimensional cases. Asymptotic theories including consistency and asymptotic normality are established. Moreover, fast computational algorithms are developed for estimation. Applications to high-dimensional stock price data and portfolio analysis are discussed. The technical proofs of the asymptotic results and the computer codes are available online.