Box–Cox transforms for realized volatility
已实现波动率的 Box–Cox 变换AI 解读 ↓
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已实现波动率的 Box–Cox 变换
- 研究问题
- 对数变换不能完全消除已实现波动率的有限样本偏度时，其他 Box–Cox 变换能否改善近似及积分波动率区间覆盖？
- 方法与思路
- 作者利用 Edgeworth 展开分析不同变换参数的准确性，推导近似消除偏度的参数，并以大量模拟比较有限样本表现。
- 材料陈述的贡献
- 摘要称，所推导变换优于对数等选择；在考察的模型中，参数为负一的倒数变换最有利于控制百分之九十五区间覆盖。
- 阅读关注点
- 应核对消除偏度参数与覆盖率最优参数的关系、参数是否依赖未知量，以及模拟模型和区间反变换的实现细节。
- 阅读边界
- 仅据所给出版社摘要，负一参数的优势限于文中考察模型，不能视为普遍最优；具体公式及覆盖误差幅度未说明。
原文摘要
The log transformation of realized volatility is often preferred to the raw version of realized volatility because of its superior finite sample properties. One of the possible explanations for this finding is the fact the skewness of the log transformed statistic is smaller than that of the raw statistic. Simulation evidence presented here shows that this is the case. It also shows that the log transform does not completely eliminate skewness in finite samples. This suggests that there may exist other nonlinear transformations that are more effective at reducing the finite sample skewness. The main goal of this paper is to study the accuracy of a new class of transformations for realized volatility based on the Box-Cox transformation. This transformation is indexed by a parameter [beta] and contains as special cases the log (when [beta]=0) and the raw (when [beta]=1) versions of realized volatility. Based on the theory of Edgeworth expansions, we study the accuracy of the Box-Cox transforms across different values of [beta]. We derive an optimal value of [beta] that approximately eliminates skewness. We then show that the corresponding Box-Cox transformed statistic outperforms other choices of [beta], including [beta]=0 (the log transformation). We provide extensive Monte Carlo simulation results to compare the finite sample properties of different Box-Cox transforms. Across the models considered in this paper, one of our conclusions is that [beta]=-1 (i.e. relying on the inverse of realized volatility also known as realized precision) is the best choice if we want to control the coverage probability of 95% level confidence intervals for integrated volatility.