5 - An investigation of the relative performance of GARCH models versus simple rules in forecasting volatility

Abstract

This chapter derives and analyses a formula for the mean square error (MSE) of a linear filter applied to forecast volatility when the proxy for “true” volatility is the squared return. This derivation allows the performance of simple forecasting models relative to generalized autoregressive conditional heteroscedasticity (GARCH) forecasts to be assessed and offers an explanation as to why simpler methods are often preferred. The results are compared with the MSE of GARCH forecasts from a simulation experiment. The results demonstrate that linear filter based forecasts can result in smaller MSE values than GARCH forecasts in some circumstances, particularly in small sample sizes where estimated GARCH parameters are inaccurate. Other proxies of volatility are considered, and an additional simulation experiment demonstrates the predictive power of GARCH. GARCH models have enjoyed significant empirical success with regard to explaining in-sample characteristics of volatility. However, out-of-sample performance appears to be very poor, with very little of the variability in ex-post returns being explained by the estimated model. GARCH forecasts are incredibly accurate at forecasting the unobservable conditional volatility, but if forecasting squared returns is the aim then other models may be able to better the GARCH forecasts. The empirical study conducted demonstrates the relevance of the preceding analysis, and shows that GARCH models can perform well out-of-sample, particularly when modeling daily volatility or when modeling monthly “realized” volatility.