Model specification for volatility forecasting benchmark

The ideal model specification for asset price volatility forecasting is still an open question. From a variable transformation perspective, existing studies arbitrarily choose between the raw volatility measure, its square root form, or its natural logarithmic form. In this paper, both the in- and out-of-sample forecasting results support the effectiveness of variable transformation compared to the raw volatility variable. Notably, the logarithmic transformation shows overwhelming advantages. Our results hold across thirty global stock indices, five cryptocurrencies, a crude oil market, as well as a wide range of extensions and robustness checks. In statistics, we find the predictability sources that the logarithmic transformation can lead to more efficient regression estimators by mitigating the heteroscedasticity and serial correlation issues. Consequently, let's make a deal: the benchmark model of volatility forecasting should be based on the natural logarithmic form of the original volatility measure.