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

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 volatilityWishart 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.