Elliptically Symmetric Principal Component Analysis: Modeling Temporal/contemporaneous Dependence Using Non-gaussian Distributions

Abstract

The primary objective of this paper is to extend the classical principal component analysis (PCA), aiming to reduce the dimensionality of a large number of Normal interrelated variables, in two directions: The rst is to go beyond the static (contem- poraneous or synchronous) covariance matrix among these interrelated variables to include certain forms of temporal (over time) dependence. The second direction takes the form of extending the PCA model beyond the multivariate normal distribution to the elliptically symmetric family of distributions, including the Normal, Student's t, the Laplace, and the Pearson type II distributions as special cases. The result of these extensions is called the elliptically symmetric principal component analysis (ESPCA), which is illustrated using Monte Carlo simulations to demonstrate the enhanced relia- bility of these more general factor models in the context of out-of-sample forecasting.