Likelihood Inferences for High-Dimensional Factor Analysis of Time Series With Applications in Finance

We develop a matrix decomposition technique 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.

We establish asymptotic theories, including consistency and asymptotic normality. Moreover, fast computational algorithms are developed for estimation. Applications to high-dimensional stock price data and portfolio analysis are discussed.