Formal GARCH performance in a computable dynamic general equilibrium framework

Abstract

This study uses a Computable Dynamic General Equilibrium setting based on Brock’s (1979, 1982) intertemporal growth and asset pricing models and applies this framework as a formal test to study the out-of-sample forecast performance of Bollerslev’s (1986) GARCH (1,1) Classical Historical Volatility forecasts. The solution to Brock’s growth model reflects the utility maximizing behavior of the consumer and profit maximizing behavior of producers, and is a framework that has recorded some remarkable successes in mirroring the real economy. All existing studies have used a sample realized variance in the forecast horizon to test the out-of- sample performance of conditional variance forecasting models. The realized variance is simply an approximation to the true distribution of variance in the forecast horizon, and is often an unfair benchmark of performance. Simulation of Brock’s model enables one to obtain the true distribution of asset returns and their variance at all times. The true distribution reflects all the possible states of a simulated economy, which is shown to mimic all the properties observed in empirical financial data. This framework affords the luxury of comparing the out-of-sample forecasts from various models with the true variance in the forecast horizon. The results jointly demonstrate that the GARCH (1,1) model performs significantly better than the Classical Historical Volatility when the true variance is used as the forecast comparison benchmark. It is concluded that the use of realized variance for out-of-sample performance is highly misleading, especially for short-run forecasts.