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

近年来，在许多奋进领域，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看到新数据在几分之一毫秒内到达。HFD发生在医学、金融和经济学、与环境有关的某些记录中，也许还发生在其他领域。研究通常关注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，该项目已经发现了一种新的方式来看待控制HFD系统状态的参数之间的依赖关系。新的相关性结构允许从相邻时期借用信息，如果有一组数据，也可以从其他系列借用信息。该项目正在探讨这一新办法的后果。该研究在高频数据的统计处理方面产生了变革性的改进。新的方法来看待依赖性涉及的一系列表示的普通积分的帮助下，随机积分。这允许使用高频回归技术来连接相邻时间间隔中的信息。这是在不改变现有模式的情况下实现的。这具有深远的影响，导致更有效的估计，更好的预测，并在准确性方面，更系统地处理标准误差的估计。模型选择也将得到极大的便利。该方法不依赖于时间或小组规模大，也不依赖于假设，如平稳的数据序列。所有新的依赖关系可以从相关时间段内的高频数据一致地估计。效率增益至少接近50%，因此现有的效率界限将变得无关紧要。预计这种方法将形成高频数据的新范例。除了开发一般理论外，该项目还关注金融数据的应用。应用的兴趣量包括已实现的每日波动率、相关性、杠杆效应、波动风险、跳跃分数等。我们还致力于风险管理、预测和投资组合管理的应用。更精确的估计，改进标准误差，将是有用的，在所有这些金融领域。主流投资者、监管机构和政策制定者对结果感兴趣，结果完全属于公共领域。依赖结构也可以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.