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The paper uses the daily stock market index returns of Fama–French to attempt a comparative forecasting analysis of different volatility models. The comparison naturally pre-requests the specification of the competing volatility frameworks and therefore the paper among other issues deals with dilemmas about whether volatility–return relations hold. As expected the analysis focuses on FIEGARCH-M models that extend the basic long memory volatility framework of  Bollerslev and Mikkelsen (1996 . “Modeling and Pricing Long Memory in Stock Market Volatility.”  Journal of Econometrics  73:151–84) with the introduction of a volatility in mean effect. Taking also into consideration the work of  Christensen, Nielsen, and Zhu (2007 . “The Effect of Long Memory in Volatility of Stock Market Fluctuations.”  Review of Economics and Statistics  89:684–700)for the existence of spillover effects when conditional in mean equations hold a stationary and a long memory component the analysis estimates the filter long memory volatility models FIEGARCH-MG and FIEGARCH-MH presented in  Christensen, Nielsen, and Zhu (2010 . “Long Memory in Stock Market Volatility and the Volatility-in-Mean Effect: The FIEGARCH-M Model.”  Journal of Econometrics  155:170–87) in order to test whether such filter adjustments can improve volatility forecasting. Although there is no particular reason to assume that the stationary inputs in the return equations will necessarily follow the normal distribution that  Christensen, Nielsen, and Zhu (2010 . “Long Memory in Stock Market Volatility and the Volatility-in-Mean Effect: The FIEGARCH-M Model.” Journal of Econometrics 155:170–87) assume, the paper follows this path but nevertheless enriches this aspect of the analysis by introducing alternative distributional assumptions. The results indicate the existence of a statistically significant mean effect when both filter models are estimated under the assumption of t-student distribution, although as far as volatility forecasting is concerned both filtered models cannot outperform in terms of forecasting criteria the parsimonious FIEGARCH version that dominates filter and non-filter volatility models under various forecasting horizons.

Forecasting Volatility and the Risk–Return Tradeoff: An Application on the Fama–French Benchmark Market Return