Model Averaging Estimation for Conditional Volatility Models

This paper is concerned with the model averaging estimation for the conditional volatility model family. We propose a model averaging estimator for the conditional volatility under a framework of zero conditional mean and construct the corresponding weight choosing criterion. It is shown that the weight selected by the criterion asymptotically minimizes the true KL divergence as well as the Itakura-Saito distance. The forecast of the conditional volatility is also constructed under the model averaging framework. As a generalization, we extend the method to the framework where both the conditional mean and volatility require estimation. On this condition, we propose the double-weight averaging estimator that assigns separate weights to the conditional mean and volatility. Monte Carlo experiments are in favor of our newly-proposed method. For empirical application, we apply the model averaging method to the forecast of the daily volatility of Shanghai Composite Index and Shenzhen Composite Index between March 10, 2016 and June 1, 2018. We find that compared with other commonly-used methods, the model averaging forecast leads to the highest forecast accuracy even under different loss functions