Model uncertainty and forecast combination in high dimensional multivariate volatility prediction

Abstract. The identication of the optimal forecasting model for multivariate volatility prediction is not always feasible due to the curse of dimensionality typically aecting multivariate volatility models. In practice only a subset of the potentially available models can be eectively estimated after imposing severe constraints on the dynamic structure of the volatility process. This situation leaves scope for the application of forecast combination strategies as a tool for improving the predictive accuracy. Aim of the paper is to propose some alternative combination strategies and compare their performances in forecasting high dimensional multivariate conditional covariance matrices for a portfolio of US stock returns. In particular, we will consider the combination of volatility predictions generated by multivariate GARCH models, based on daily returns, and dynamic models for realized covariance matrices, built from intra-daily returns.