“粗糙”HAR模型

中文摘要 AI 辅助

本文提出了对已实现方差（RV）的粗糙连续时间模型的离散时间近似。主要的粗糙模型可以被视为由分数高斯噪声驱动的自回归过程。我们证明，当赫斯特参数低于二分之一时，该噪声的Wold表示将其依赖性集中在一阶滞后上。因此，在自回归（AR）和异质自回归（HAR）模型中增加一阶移动平均（MA(1)）分量可以近似粗糙性，并且MA系数几乎线性地映射到赫斯特参数。我们将这些扩展称为“粗糙”AR和“粗糙”HAR模型。在十个ETF的对数RV上估计这些模型，我们发现每个资产都有负的MA系数，并且隐含的赫斯特参数与连续时间模型的估计值紧密对齐。在HAR文献中，负的MA(1)分量是一个重要的特征，但在很大程度上被忽视了。在样本外比较中，“粗糙”模型在几乎所有资产和预测期限上都优于其经典对应模型，在短期预测期限上收益最大，并且其精度与粗糙连续时间模型相当，但通过标准的现成软件估计要容易得多。

英文摘要

This paper proposes discrete-time approximations to rough continuous-time models of realized variance (RV). The leading rough models can be viewed as autoregressive processes driven by fractional Gaussian noise. We show that the Wold representation of this noise concentrates its dependence at the first lag when the Hurst parameter is below one half. Augmenting the autoregressive (AR) and heterogeneous autoregressive (HAR) models with a first-order moving-average (MA(1)) component therefore approximates the roughness, and the MA coefficient maps almost linearly into the Hurst parameter. We refer to these extensions as the "rough" AR and "rough" HAR models. Estimating them on the log RV of ten ETFs, we find negative MA coefficients for every asset, and the implied Hurst parameters align closely with the estimates from the continuous-time models. In the HAR literature, the negative MA(1) component is a significant feature that has been largely overlooked. In out-of-sample comparisons, the "rough" models outperform their classical counterparts for nearly every asset and horizon, with the largest gains at short horizons, and their accuracy is comparable to that of the rough continuous-time models but much easier to estimate by standard off-the-shelf software.

发表机构

• Aarhus University（奥胡斯大学）
• Danish Finance Institute (DFI)（丹麦金融研究所）
• University of Macau（澳门大学）
• Sun Yat-sen University（中山大学）

机构由 AI 辅助整理，请以论文原文为准。