A stochastic variance factor model for large datasets and an application to S&P data

The aim of this paper is to consider multivariate stochastic volatility models for large dimensional datasets. For this purpose we use a common factor approach along the lines of Harvey, Ruiz, and Shephard (1994). More recently, Bayesian estimation methods, relying on Markov Chain Monte Carlo, have been put forward by Chib, Nardari, and Shephard (2006) to estimate relatively large multivariate stochastic volatility models. However, computational constraints can be binding when dealing with very large datasets such as, e.g., S&P 500 constituents. For instance, the Bayesian modelling approach put forward by Chib, Nardari, and Shephard (2006) is illustrated by modelling a dataset of only 20 series of stock returns. Recently, Stock and Watson (2002) have shown that principal component estimates of the common factor underlying large datasets can be used successfully in forecasting conditional means. We propose the use of principal component estimation for the volatility processes of large datasets. A Monte Carlo study and an application to the modelling of the volatilities of the S&P constituents illustrate the usefulness of our approach.