Optimal Nonparametric Methods for Ito Processes Based on High-Frequency Data

该项目将开发新的统计方法来分析内在地随时间演变的随机现象。这些方法将基于对所研究现象的高频监测，这在金融、气象、生物、神经科学、湍流、统计物理、地震学和电信等许多领域都有广泛的用途。因此，这项研究将促进应用科学家和统计学家之间的更多互动。该项目的研究和教育内容还将作为本科生和研究生的培训工具，组成涉及各级的协同研究小组。非参数方法是减少模型误判误差的有力统计工具，而基于高频的统计分析是估计连续时间随机过程精细统计特征的自然途径。虽然结合这两种方法的文献在过去的二十年里有了显著的增长，但相对较少的工作是分析和校正方法对调整参数的敏感性。该项目将通过以下方式满足这些需求：(I)开发在杠杆和微观结构噪声存在的情况下对Ito过程的现货波动率进行最优核估计的统一方法；(Ii)通过对过程的增量或小波系数进行阈值处理或收缩，设计在随机波动和无限跳跃活动存在的情况下的最优跳跃检测和集成方差估计方法；(Iii)为最优方案产生的数据驱动的封堵实施方法建立理论保证。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The project will develop new statistical methods to analyze stochastic phenomena that inherently evolves in time. The methods will be based on high-frequency monitoring of the phenomena under study, which is of widening use in many fields such as finance, meteorology, biology, neuroscience, turbulence, statistical physics, seismology, and telecommunication. Thus, the research will foster more interaction between applied scientists and statisticians. The research and educational elements of the project will also serve as a training tool for both undergraduate and graduate students by forming synergistic research groups involving all levels. Nonparametric methods are powerful statistical tools to reduce the model misspecification error, and high-frequency-based statistical analysis is a natural route to take when estimating the fine statistical features of continuous-time stochastic processes. Though the literature combining these two approaches has grown significantly during the last two decades, comparatively little work has been done to analyze and correct the sensitivity of methods to tuning parameters. The project will address these needs by (i) developing a unified approach for optimal kernel estimation of the spot volatility of an Ito process in the presence of leverage and microstructure noise; (ii) devising of optimal jump detection and integrated variance estimation methods, under the presence of stochastic volatility and infinite jump activity, via thresholding or shrinkage of the process' increments or wavelet coefficients; (iii) establishing theoretical guarantees for the data-driven plugging implementation methods resulting from the optimal schemes.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.