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.

中文翻译：

---

波动率预测基准的模型规范


资产价格波动预测的理想模型规范仍然是一个悬而未决的问题。从变量变换的角度来看，现有研究在原始波动率测度、平方根形式或自然对数形式之间任意选择。在本文中，与原始波动率变量相比，样本内和样本外预测结果都支持变量转换的有效性。值得注意的是，对数变换显示出压倒性的优势。我们的结果涵盖 30 个全球股票指数、5 种加密货币、原油市场，以及广泛的扩展和稳健性检查。在统计学中，我们发现了对数变换可以通过缓解异方差性和序列相关性问题来导致更有效的回归估计器的可预测性来源。因此，让我们做个交易：波动率预测的基准模型应该基于原始波动率度量的自然对数形式。