Model Selection and Testing of Conditional and Stochastic Volatility Models

Abstract

This paper focuses on the selection and comparison of alternative non-nested volatility models. We review the traditional in-sample methods commonly applied in the volatility framework, namely diagnostic checking procedures, information criteria, and conditions for the existence of moments and asymptotic theory, as well as the out-of-sample model selection approaches, such as mean squared error and Model Confidence Set approaches. The paper develops some innovative loss functions which are based on Value-at-Risk forecasts. Finally, we present an empirical application based on simple univariate volatility models, namely GARCH, GJR, EGARCH, and Stochastic Volatility that are widely used to capture asymmetry and leverage.

Keywords: Volatility Model Selection, Volatility Model Comparison, Non-Nested Models, Model Confidence Set, Value-At-Risk Forecasts, Asymmetry, Leverage

JEL Classification: C11, C22, C52, C58