The promising empirical results presented using high-frequency data show that the logvolatility behaves essentially as a fractional Brownian motion (fBm) with a Hurst exponent smaller than 0.5. Motivated by these findings, we propose the autoregressive rough volatility (ARRV) model, which combines the fractional Gaussian noise (fGn) process and time series models to forecast volatility. We apply this model to the VIX index by adopting the fBm approximation technique, and our results indicate that the ARRV model can significantly improve VIX out-of-sample forecast accuracy, particularly during turbulent times.

中文翻译：

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具有规律性修改的波动率预测

使用高频数据呈现的有希望的实证结果表明，对数波动率本质上表现为 Hurst 指数小于 0.5 的分数布朗运动 (fBm)。受这些发现的启发，我们提出了自回归粗略波动率 (ARRV) 模型，该模型结合分数高斯噪声 (fGn) 过程和时间序列模型来预测波动率。我们通过采用 fBm 近似技术将该模型应用于 VIX 指数，我们的结果表明 ARRV 模型可以显着提高 VIX 样本外预测的准确性，特别是在动荡时期。