Direct Versus Iterated Multi-Period Volatility Forecasts

Multi-period-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 paper, we compare several approaches of producing multi-period-ahead forecasts within the GARCH and 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 of equity, Treasury, currency, and commodity indices. While the underlying data is available at high-frequency (5-minutes), we are interested at forecasting variances 5, 10, 22, 44, and 66 days ahead. The empirical analysis, which is carried in-sample and out-of-sample with data from 2005 to 2018, yields the following results. For GARCH, iterated GARCH dominates the direct GARCH approach. In the case of RV, the direct RV is preferred to the iterated RV. This dichotomy of results emphasizes the need for an 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 the variance, 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.