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. We suggest the use of the principal component methodology of Stock and Watson [Stock, J.H., Watson, M.W., 2002. Macroeconomic forecasting using diffusion indices. Journal of Business and Economic Statistics, 20, 147\u2013162] for the stochastic volatility factor model discussed by Harvey, Ruiz, and Shephard [Harvey, A.C.,Ruiz, E., Shephard, N., 1994. Multivariate Stochastic Variance Models. Review of Economic Studies, 61, 247\u2013264]. We provide theoretical and Monte Carlo results on this method and apply it to S&P data