Multi-Period Forecasts of Volatility: Direct, Iterated, and Mixed-Data Approaches

Multi-period forecasts of stock market return volatilities are often used in many applied areas of finance where long horizon measures of risk are necessary. Yet, very little is known about how to forecast variances several periods ahead, as most of the focus has been placed on one-period ahead forecasts. In this paper, we compare several approaches of producing multi-period ahead forecasts -iterated, direct, and mixed data sampling (MIDAS)- as alternatives to the often-used "scaling-up" method. The comparison is conducted (pseudo) out-of-sample using returns data of the US stock market portfolio and a cross section of size and book-to-market portfolios. The comparison results are surprisingly sharp. For the market, size, and book-to-market portfolios, we obtain the same precision ordering of the forecasting methods. The direct approach provides the worse (in MSFE sense) forecasts; it is dominated even by the naive "scaling-up" method. Iterated forecasts are suitable for shorter horizons (5 to 10 periods ahead), but their MSFEs deteriorate as the horizon increases. The MIDAS forecasts perform well at long horizons: they dominate all other approaches at horizons of 10-periods ahead and higher. The MIDAS forecasting advantage becomes most apparent at horizons of 30-periods ahead and longer. In sum, this study dispels the notion that volatility is not forecastable at long horizons and offers an approach that delivers accurate pseudo out-of-sample predictions.

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