A forecast-based comparison of restricted Wishart autoregressive models for realized covariance matrices

Abstract

Models for realized covariance matrices may suffer from the curse of dimensionality as more traditional multivariate volatility models (such as GARCH and stochastic volatility). Within the class of realized covariance models, we focus on the Wishart specification introduced by C. Gourieroux, J. Jasiak, and R. Sufana [2009. The Wishart autoregressive process of multivariate stochastic volatility. Journal of Econometrics 150, no. 2: 167–81] and analyze here the forecasting performances of the parametric restrictions discussed in M. Bonato [2009. Estimating the degrees of freedom of the realized volatility Wishart autoregressive model. Manuscript available at http://ssrn.com/abstract=1357044], which are motivated by asset features such as their economic sector and book-to-market or price-to-earnings ratios, among others. Our purpose is to verify if restricted model forecasts are statistically equivalent to full-model specification, a result that would support the use of restrictions when the problem cross-sectional dimension is large.

Keywords:

• realized covariance
• WAR
• HAR
• multivariate volatility forecasts

JEL Classifications: :

• C32
• C53
• C52

Acknowledgements

This article was written while the second author was visiting the Chiang Mai University, Faculty of Economics, Thailand, whose hospitality is gratefully acknowledged. The views expressed herein are those of the authors and not necessarily those of the Swiss National Bank or of Credit Suisse, which do not accept any responsibility for the contents and opinions expressed in this paper.