Multi-period forecasts of stock market return volatilities are often used in asset pricing, portfolio allocation, risk-management and most other areas of finance where longhorizon measures of risk are necessary. Yet, very little is known about how to forecast volatility several periods ahead, as most of the focus has been on one-period-ahead forecasts. In this paper, we compare several approaches of producing multi-period ahead forecasts of volatility – iterated, direct, and mixed-data sampling (MIDAS) – as alternatives to the often-used “scaling ” method. The comparison is conducted (pseudo) out-of-sample using returns data of the US stock market portfolio and a cross section of size, book-to-market, and industry portfolios. The results are surprisingly sharp. For the market and all other portfolios, we obtain the same ordering of the volatility forecasting methods. The direct approach provides the worse (in MSFE sense) forecasts; it is dominated even by the naive scaling method. Iterated forecasts are suitable for shorter horizons (5 to 10 days ahead), but their MSFEs deteriorate rapidly as the horizon increases. The MIDAS forecasts perform well at long horizons
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