A0948
Title: Factor analysis for heavy-tailed, heteroscedastic data
Authors: Chang Yuan Li - University of California, Santa Barbara (United States) [presenting]
Alexander Shkolnik - University of California, Santa Barbara (United States)
Abstract: Factor analysis of financial asset returns aims to decompose a return covariance matrix into systematic and specific components. One or both of these components are believed to have considerably heavier tails than the Gaussian distribution. Traditional statistical approaches like PCA and MLE suffer from drawbacks: sensitivity to outliers, and strict assumptions on the underlying distributions. And so, these are often not suitable for the purpose of decomposing financial asset returns. We propose a convex optimization procedure to decompose a security return covariance into its low rank and diagonal parts. The diagonal parts, corrupted by outliers, can be improved by weighted ridge regression and outlier correction methods. By doing so, the low-rank estimate can be improved as well. We illustrate the results with some analytical examples as well as simulated and empirical models.
