Evaluating the Forecasting Performance of GARCH Models Using White’s Reality Check

Abstract

The important issue of forecasting volatilities brings the difficult task of back-testing the forecasting performance. As volatility cannot be observed directly, one has to use an observable proxy for volatility or a utility function to assess the prediction quality. This kind of procedure can easily lead to poor assessment. The goal of this paper is to compare different volatility models and different performance measures using White’s Reality Check. The Reality Check consists of a non-parametric test that checks if any of a number of concurrent methods yields forecasts significantly better than a given benchmark method. For this purpose, a Monte Carlo simulation is carried out with four different processes, one of them a Gaussian white noise and the others following GARCH specifications. Two benchmark methods are used: the naive (predicting the out-of-sample volatility by in-sample variance) and the Riskmetrics method