Collaborative Research: Better efficiency, better forecasting, better accuracy: A new light on the dependence structure in high frequency data

近年来，在许多领域，数据的可用性和规模都出现了爆炸式增长；这种现象通常被称为大数据。该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新数据。HFD出现在医学、金融和经济、与环境有关的某些录音中，也许还出现在其他领域。研究通常关注的是如何将这些数据转化为知识，而这正是当前项目将提供帮助的地方。具体来说，该项目发现了一种新的方法来研究控制HFD系统状态的参数之间的依赖关系。新的依赖结构允许从相邻的时间段借用信息，如果有一个数据面板，也可以从其他序列借用信息。该项目正在探索这种新方法的后果。这项研究在高频数据的统计处理方面产生了变革性的改进。研究相关性的新方法涉及到用随机积分表示一系列普通积分。这允许使用高频回归技术将相邻时间间隔内的信息连接起来。它是在不改变现有模型的情况下实现的。这具有深远的影响，导致更有效的估计器，更好的预测，并且，就准确性而言，对标准误差估计的更系统的处理。模型选择也将大大方便。该方法不依赖于时间或面板大小；它也不依赖于数据序列的平稳性等假设。所有新的依赖关系都可以从相关时间段内的高频数据中一致地估计出来。效率收益至少接近50%，因此现有的效率界限将变得无关紧要。预计该方法将形成高频数据的新范式。除了发展一般理论外，该项目还涉及财务数据的应用。应用的兴趣量包括已实现的每日波动率、相关性、杠杆效应、波动率风险、跳跃的比例等等。我们还研究风险管理、预测和投资组合管理的应用程序。在所有这些金融领域，标准误差得到改善的更精确的估计值将是有用的。主要投资者、监管机构和政策制定者都对其研究结果感兴趣，而且研究结果完全属于公共领域。依赖结构也应用于其他具有高频数据的研究领域，包括医学、神经科学和湍流。

Recent years have seen an explosion in the availability and size of data in many areas of endeavor; the phenomenon is often referred to as big data. This project is concerned with a particular form of such data, namely high frequency data (HFD), where series of observations can see new data to arrive in fractions of milliseconds. HFD occurs in medicine, in finance and economics, in certain recordings relating to the environment, and perhaps in other areas. Research is often concerned with how to turn this data into knowledge, and this is where the current project will help. Specifically, the project has discovered a new way to look at the dependence relationships between the parameters governing the state of the HFD system. The new dependence structure permits the borrowing of information from adjacent time periods, and also from other series if one has a panel of data. The consequences of this new approach are being explored by the project. The research produces transformational improvements in the statistical handling of high frequency data.The new way to look at dependence involves the representation of series of ordinary integrals with the help of stochastic integrals. This permits the use of high frequency regression techniques to connect the information in adjacent time intervals. It is achieved without altering current models. This has far-reaching consequences, leading to more efficient estimators, better prediction, and, in terms of accuracy, a more systematic treatment of the estimation of standard errors. Model selection will also be greatly facilitated. The methodology does not depend on either time or panel size being large; neither does it depend on assumptions such as stationarity of the data series. All the new dependence relationships can be consistently estimated from high frequency data inside the relevant time periods. Efficiency gains are at the very least close to 50%, and thus existing efficiency bounds will become irrelevant. It is expected that this approach will form a new paradigm for high frequency data. In addition to developing a general theory, the project is concerned with applications to financial data. Applied quantities of interest include realized daily volatility, correlations, leverage effect, volatility risk, fraction of jumps, and so on. We also work on applications to risk management, forecasting, and portfolio management. More precise estimators, with improved standard errors, will be useful in all these areas of finance. The results are of interest to main-street investors, regulators and policymakers, and the results are entirely in the public domain. The dependence structure also has application in other areas of research that have high frequency data, including medicine, neural science, and turbulence.