Assessing the Performance of a Prediction Error Criterion Model Selection Algorithm in the Context of ARCH Models

Autoregressive conditional heteroscedasticity (ARCH) models have successfully been applied in order to predict asset return volatility. Predicting volatility is of great importance in pricing financial derivatives, selecting portfolios, measuring and managing investment risk more accurately. In this paper, a number of ARCH models are considered in the framework of evaluating the performance of a method for model selection based on a standardized prediction error criterion (SPEC). According to this method, the ARCH model with the lowest sum of squared standardized forecasting errors is selected for predicting future volatility. A number of statistical criteria, that measure the distance between predicted and inter-day realized volatility, are used to examine the performance of a model to predict future volatility, for forecasting horizons ranging from one day to one hundred days ahead. The results reveal that the SPEC model selection procedure has a satisfactory performance in picking that model that generates “better” volatility predictions. A comparison of the SPEC algorithm with a set of other model evaluation criteria yields similar findings. It appears, therefore, that it can be regarded as a tool in guiding one’s choice of the appropriate model for predicting future volatility, with applications in evaluating portfolios, managing financial risk and creating speculative strategies with options.