Two are better than one: Volatility forecasting using multiplicative component GARCH‐MIDAS models

We examine the properties and forecast performance of multiplicative volatility specifications that belong to the class of generalized autoregressive conditional heteroskedasticity–mixed‐data sampling (GARCH‐MIDAS) models suggested in Engle, Ghysels, and Sohn (Review of Economics and Statistics, 2013, 95, 776–797). In those models volatility is decomposed into a short‐term GARCH component and a long‐term component that is driven by an explanatory variable. We derive the kurtosis of returns, the autocorrelation function of squared returns, and the R2 of a Mincer–Zarnowitz regression and evaluate the QMLE and forecast performance of these models in a Monte Carlo simulation. For S&P 500 data, we compare the forecast performance of GARCH‐MIDAS models with a wide range of competitor models such as HAR (heterogeneous autoregression), realized GARCH, HEAVY (high‐frequency‐based volatility) and Markov‐switching GARCH. Our results show that the GARCH‐MIDAS based on housing starts as an explanatory variable significantly outperforms all competitor models at forecast horizons of 2 and 3 months ahead.