长时间尺度与短时间尺度：艰难的困境及超越
Long vs Short Time Scales: the Rough Dilemma and Beyond
摘要：
使用一个大型数据集的主要外汇汇率，我们测试的鲁棒性粗糙分数波动率模型在不同的时间尺度，包括平滑和测量误差的分析。我们的研究结果导致新的程式化的事实，在对数-对数图的二阶矩实现方差增量对滞后表现出一定的凸性，除了粗糙度和平稳性的波动。在小尺度下感知到的非常低的赫斯特指数与粗略的框架一致，而在较大尺度下感知到的较高的赫斯特指数导致迄今为止引入的模型尚未描述的双对数图的非线性行为。
英文摘要：
Using a large dataset on major FX rates, we test the robustness of the rough fractional volatility model over different time scales, by including smoothing and measurement errors into the analysis. Our findings lead to new stylized facts in the log-log plots of the second moments of realized variance increments against lag which exhibit some convexity in addition to the roughness and stationarity of the volatility. The very low perceived Hurst exponents at small scales is consistent with the rough framework, while the higher perceived Hurst exponents for larger scales leads to a nonlinear behavior of the log-log plot that has not been described by models introduced so far.
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