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带变点检测的稀疏高频波动率估计

文章 arXiv papers · 作者: Greeshma Balabhadra et al.
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总结

本文提出稀疏高频波动率估计方法，旨在现货波动率突然变化时仍保持稳健。所提估计方法对现有方法施加 ℓ1 惩罚，重点研究幂变差估计量这一衡量波动率的基础类别。作者证明了对潜在未观测波动率及其变点位置进行估计的一致性，特定估计量还达到了极小极大收敛率。

在计算上，该方法使用最小角回归估计候选变点，再通过缩减后的动态规划步骤确定其数量。数值结果显示，该方法速度快，并能准确检测样本末端附近的断点。样本外预测中，据称这些估计量能生成更平滑、更真实的波动率预测，并在不同采样频率和预测期限下优于广泛的经典及近期替代方法。所提供的描述未列出具体数据集、基准或数值表现，因此无法独立评估这些比较。

核心观点

  • 估计量采用 ℓ1 正则化，使高频波动率估计具有稀疏性，并能稳健应对突变。
  • 本文研究幂变差估计量，并证明了波动率及变点位置估计的一致性。
  • 最小角回归用于寻找候选变点，缩减后的动态规划用于确定其数量。
  • 作者称其能准确检测样本末端附近的断点，并改善不同频率和期限下的样本外预测。

标签

波动率统计学机器学习高频交易
全文
# High-Frequency Volatility Estimation with Fast Multiple Change Points Detection


# High-Frequency Volatility Estimation with Fast Multiple Change Points Detection









We propose a method for constructing sparse high-frequency volatility estimators that are robust against change points in the spot volatility process. The estimators we propose are $\ell_1$-regularized versions of existing volatility estimators. We focus on power variation estimators as they represent a fundamental class of volatility estimators. We establish consistency of these estimators for the true unobserved volatility and the change points locations, showing that minimax rates can be achieved for particular volatility estimators. The new estimators utilize the computationally efficient least angle regression algorithm for estimation purposes, followed by a reduced dynamic programming step to refine the final number of change points. In terms of numerical performance, these estimators are not only computationally fast but also accurately identify breakpoints near the end of the sample, both features highly desirable in today's electronic trading environment. In terms of out-of-sample volatility prediction, our new estimators provide more realistic and smoother volatility forecasts, outperforming a broad range of classical and recent volatility estimators across various frequencies and forecasting horizons.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。