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.