Direct Versus Iterated Multi-Period Volatility Forecasts: Why MIDAS Is King

Abstract

Multiperiod-ahead forecasts of returns’ variance are used in most areas of applied finance where long-horizon measures of risk are necessary. Yet, the major focus in the variance forecasting literature has been on one-period-ahead forecasts. In this review, we compare several approaches of producing multiperiod-ahead forecasts within the generalized autoregressive conditional heteroscedastic (GARCH) and realized volatility (RV) families—iterated, direct, and scaled short-horizon forecasts. We also consider the newer class of mixed data sampling (MIDAS) methods. We carry the comparison on 30 assets, comprising equity, Treasury, currency, and commodity indices. While the underlying data are available at high frequency (5 minutes), we are interested in forecasting variances 5, 10, 22, 44, and 66 days ahead. The empirical analysis, which is performed in sample and out of sample with data from 2005 to 2018, yields the following results: Iterated GARCH dominates the direct GARCH approach, and the direct RV is preferred to the iterated RV. This dichotomy of results emphasizes the need foran approach that uses the richness of high-frequency data and, at the same time, produces a direct forecast of the variance at the desired horizon, without iterating. The MIDAS is such an approach, and unsurprisingly, it yields the most precise forecasts of variance both in and out of sample. More broadly, our study dispels the notion that volatility is not forecastable at long horizons and offers an approach that delivers accurate out-of-sample predictions.