Collaborative Research: Statistical Inference for High-Frequency Data

为了实现大数据革命的前景，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），其中一系列观察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、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，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，以揭示控制HFD系统的依赖结构。新的依赖关系结构将允许从相邻的时间段“借用”信息，也允许从一组数据的其他序列“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HFD的新范式。除了开发一般理论之外，该项目还关注财务数据的应用，包括风险管理、预测和投资组合管理。在所有这些金融领域，更精确的估计值（误差范围更小）都将是有用的。预计其结果将引起投资者、监管机构和政策制定者的兴趣，而且其结果完全属于公共领域。该项目的目标是在将观测值和参数过程划分为块的基础上，为高频数据中的推理创建一个统一的框架。这项工作有两条路径，都涉及数据体系结构的基本结构。“块内”方法使用邻近性使观察结果的结构在局部邻域中更易于访问。“块之间”方法建立了一种工具，可以使用随机微积分来研究相邻块（在时间和空间上）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型的情况下实现的。项目的最后一部分致力于进一步研究观测到的渐近方差，特别是在调整参数和推理解释方面的工作。“块内”和“块间”方法的制定都涵盖了通常从高频数据序列中估计的一般时变“参数”，不仅包括波动性，还包括偏度（杠杆效应）、回归系数和参数动态（如波动性的波动性）。在这两种情况下，除了高频率观测外，观测数据和参数过程可能具有大尺寸（大面板尺寸）。块内方法允许对潜在的潜在过程和微观结构/观察噪声联合声明相邻性。对于between block方法，研究人员将进一步开发一种新的方法来研究参数之间的依赖关系。

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.