This paper is concerned with model averaging estimation for conditional volatility models. Given a set of candidate models with different functional forms, we propose a model averaging estimator and forecast for conditional volatility, and construct the corresponding weight‐choosing criterion. Under some regulatory conditions, we show that the weight selected by the criterion asymptotically minimizes the true Kullback–Leibler divergence, which is the distributional approximation error, as well as the Itakura–Saito distance, which is the distance between the true and estimated or forecast conditional volatility. Monte Carlo experiments support our newly proposed method. As for the empirical applications of our method, we investigate a total of nine major stock market indices and make a 1‐day‐ahead volatility forecast for each data set. Empirical results show that the model averaging forecast achieves the highest accuracy in terms of all types of loss functions in most cases, which captures the movement of the unknown true conditional volatility.

中文翻译：

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条件波动率模型的模型平均估计及其在股市波动率预测中的应用

本文涉及条件波动率模型的模型平均估计。给定一组具有不同功能形式的候选模型，我们提出了一个模型平均估计器和条件波动率预测，并构造了相应的权重选择标准。在某些监管条件下，我们表明，根据准则选择的权重渐近最小化了真实的Kullback-Leibler散度（即分布近似误差）以及Itakura-Saito距离（即真实值与估计值或预测值之间的距离）有条件的波动。蒙特卡洛实验支持我们新提出的方法。至于我们方法的经验应用，我们总共调查了九种主要股市指数，并对每个数据集进行了为期1天的提前波动预测。