Collaborative Research: Statistical Inference for High-Frequency Data

合作研究：高频数据的统计推断

• 批准号: 1713118
• 负责人: Lan Zhang
• 金额: $ 14.06万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-07-01 至 2021-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1713118&HistoricalAwards=false
• 关键词: Collaborative; Research; Statistical; Inference; Frequency

To pursue the promise of the big data revolution, the current project is concerned with a particular form of such data, high frequency data (HFD), where series of observations can see data updates in fractions of milliseconds. With technological advances in data collection, HFD occurs in medicine (from neuroscience to patient care), finance and economics, geosciences (such as earthquake data), marine science (fishing and shipping), and other areas. The research focuses on how to extract information from complex big data and how to turn data into knowledge. In particular, the project aims to develop cutting-edge mathematics and statistical methodology to uncover the dependence structure governing a HFD system. The new dependence structure will permit the "borrowing" of information from adjacent time periods, and also from other series from a panel of data. It is expected that the results will lead to more efficient estimators and better prediction and that this approach will form a new paradigm for HFD. In addition to developing a general theory, the project is concerned with applications to financial data, including risk management, forecasting, and portfolio management. More precise estimators, with improved margins of error, will be useful in all these areas of finance. The results are expected to be of interest to investors, regulators, and policymakers, and the results are entirely in the public domain. The goal of this project is to create a unified framework for inference in high frequency data, based on dividing the observations and the parameter process into blocks. The work pursues two paths, both involving the fundamental structure of the data architecture. A "within block" approach uses contiguity to make the structure of the observations more accessible in local neighborhoods. The "between block" approach sets up a tool for using stochastic calculus to study the relationship between parameters in blocks that are adjacent (in time and space). It also permits the integration of high and low frequency models. This is achieved without altering current models. A final part of the project is devoted to further study of the observed asymptotic variance, in particular work on tuning parameters and inferential interpretation. Both the "within block" and "between block" approaches are formulated to cover general time varying "parameters" that are usually estimated from high frequency data series, not only volatility, but also skewness (leverage effect), regression coefficients, and parameter dynamics (such as volatility of volatility). In both cases, the observed data and also parameter processes may have large dimension (large panel size) in addition to high frequency observation. The within block approach permits contiguity to be stated jointly for the latent underlying processes and the microstructure/observation noise. For the between block approach, the investigators will further develop a new way to look at the dependence relationships between the parameters.

为了实现大数据革命的承诺，目前的项目关注的是这种数据的一种特殊形式，即高频数据（HFD），其中一系列观测可以在几毫秒内看到数据更新。随着数据收集技术的进步，HFD出现在医学（从神经科学到病人护理），金融和经济学，地球科学（如地震数据），海洋科学（渔业和航运）和其他领域。研究重点是如何从复杂的大数据中提取信息，以及如何将数据转化为知识。特别是，该项目旨在开发尖端的数学和统计方法，以揭示管理HFD系统的依赖结构。新的相关性结构将允许“借用”相邻时期的信息，也可以从一组数据的其他系列中“借用”信息。预计结果将导致更有效的估计和更好的预测，这种方法将形成一个新的范式HFD。除了开发一般理论外，该项目还关注金融数据的应用，包括风险管理，预测和投资组合管理。在所有这些金融领域，更精确的估算方法，以及更好的误差幅度，都将是有用的。预计投资者、监管机构和政策制定者会对结果感兴趣，结果完全属于公共领域。该项目的目标是创建一个统一的框架，在高频数据的推理，基于划分的观察和参数过程成块。这项工作遵循两条路径，都涉及数据架构的基本结构。“块内”方法使用邻接性使观测的结构在局部邻域中更容易访问。“块之间”方法建立了一个工具，用于使用随机微积分来研究相邻（在时间和空间上）块中参数之间的关系。它还允许高频和低频模型的集成。这是在不改变现有模式的情况下实现的。该项目的最后一部分是致力于进一步研究所观察到的渐近方差，特别是调整参数和推理解释的工作。“块内”和“块间”方法都被制定为涵盖通常从高频数据序列估计的一般时变“参数”，不仅包括波动率，而且包括偏度（杠杆效应）、回归系数和参数动态（如波动率的波动率）。在这两种情况下，除了高频观察之外，观察到的数据以及参数过程可能具有大维度（大面板尺寸）。块内的方法允许连续性被联合声明为潜在的潜在过程和微观结构/观察噪声。对于块间方法，研究人员将进一步开发一种新的方法来查看参数之间的依赖关系。

项目成果

The algebra of two scales estimation, and the S-TSRV: High frequency estimation that is robust to sampling times

两种尺度估计的代数和 S-TSRV：对采样时间具有鲁棒性的高频估计

• DOI: 10.1016/j.jeconom.2018.09.007
• 发表时间: 2019
• 期刊: Journal of Econometrics
• 影响因子: 6.3
• 作者: Mykland, Per A.;Zhang, Lan;Chen, Dachuan
• 通讯作者: Chen, Dachuan

The Observed Asymptotic Variance: Hard edges, and a regression approach

观察到的渐近方差：硬边和回归方法

• DOI: 10.1016/j.jeconom.2020.07.008
• 发表时间: 2021
• 期刊: Journal of Econometrics
• 影响因子: 6.3
• 作者: Mykland, Per A.;Zhang, Lan
• 通讯作者: Zhang, Lan

The Five Trolls Under the Bridge: Principal Component Analysis With Asynchronous and Noisy High Frequency Data

桥下的五个巨魔：异步和噪声高频数据的主成分分析

• DOI: 10.1080/01621459.2019.1672555
• 发表时间: 2020
• 期刊: Journal of the American Statistical Association
• 影响因子: 3.7
• 作者: Chen, Dachuan;Mykland, Per A.;Zhang, Lan
• 通讯作者: Zhang, Lan

Supplement to: ``Assessment of of Uncertainty in High Frequency Data: The Observed Asymptotic Variance": Proofs and Technical Issues (Econometrica, Vol 85, No 1, January 2017, 197-231).

补充：“高频数据不确定性的评估：观察到的渐近方差”：证明和技术问题（《计量经济学》，第 85 卷，第 1 期，2017 年 1 月，197-231）。

• 发表时间: 2017
• 期刊: Econometrica
• 影响因子: 6.1
• 作者: Mykland, Per A;Zhang, Lan
• 通讯作者: Zhang, Lan