Statistical Inference for High Frequency Data

该项目致力于使用非参数的“潜在半鞅模型”来估计高频数据的波动率和相关数量。市场微观结构(在统计上类似于测量误差)的存在对这个问题至关重要，因为它对估计者有很大影响。这个项目要问的主要问题如下：数据中有哪些信息？根据每天的数据，甚至五分钟的数据，可以一致地估计哪些数量？对这些问题的满意回答将有助于几个目的：(1)了解研究人员希望从数据中提取什么信息(参数估计)；(2)数据压缩，因为数据量巨大，对所有相关参数的估计将提供(至少大约)对数据的“充分”总结；以及(3)更广泛的科学和社会目标，如下所述。要查看的数据包括金融交易和报价数据，在某些情况下还包括订单簿数据。高维数据也将被考虑。一个主要工具将是使用统计邻接性，这将简化和澄清数据的结构。近年来，高频金融数据的可用性呈爆炸性增长。这为每天高精度地估计波动率等数量提供了可能性。这样的估计对投资者、监管机构和政策制定者来说是非常重要的。关于这一主题的学术文献正在开发中，涉及从金融到计量经济学和统计学再到纯粹概率的不同领域。这个项目的主要主题是找到将这些数据转化为知识的方法。该项目寻求提供(经济上或其他方面的)可解释参数的估计值，而不是海量的、几乎没有结构的数据。理论方法是在连续时间金融模型的背景下看到高频数据，如用于资产定价、投资组合管理、期权交易和风险管理。到目前为止，这类模型通常依赖于假设的高频数据。通过将它们与实际的高频数据结合在一起，该项目的长期目标是建立一个既有理论又有经验的金融学“大统一理论”。作为必然结果，这有可能通过将风险管理与业务和监管决策以及数据与模型相结合来引发变革性变化。这可能有助于避免过去几年中一些最严重的无数据模型错误。高频数据的方法在金融以外也有应用，例如在神经科学和湍流领域，以及其他可以获得流数据的领域。环境科学和监测也常常以高频数据的形式出现。与此同时，时间依赖数据的似然理论(这是该项目的核心)是一种设置，它将金融和经济与包括生物和医学在内的各种科学努力联系起来，这些领域的方法之间存在相互反馈。

The project is concerned with the estimation of volatility and related quantities for high frequency data using the nonparametric "latent semi-martingale model." The existence of market microstructure (statistically similar to measurement error) is crucial to this problem as it substantially affects estimators. The main questions to be asked by this project are the following: What information is there in the data? What quantities can consistently be estimated on the basis of daily data or even five minute data? A satisfactory answer to these questions will serve several purposes: (1) an understanding of what information (parameter estimates) researchers can hope to extract from data; (2) data compression, because the amounts of data are huge, and estimation of all relevant parameters will provide an (at least approximately) "sufficient" summary of the data; and (3) broader scientific and social goals as discussed below. The data to be looked at include financial transaction and quote data and, in some circumstances, order book data. High dimensional data also will be considered. A major tool will be the use of statistical contiguity which simplifies and clarifies the structure of the data.The availability of high frequency financial data has exploded in recent years. This has opened the possibility of estimating quantities like volatility on a daily basis with high precision. Such estimates are of substantial interest to investors, regulators, and policymakers. An academic literature on this topic is in development, drawing on diverse areas ranging from finance via econometrics and statistics to pure probability. The main topic of this project is to find ways of turning these data into knowledge. Instead of massive, barely structured data, the project seeks to provide estimators of (economically or otherwise) interpretable parameters. The theoretical approach is to see the high frequency data in the context of continuous-time finance models, as used in asset pricing, portfolio management, options trading, and risk management. So far, such models have often relied on hypothetical high frequency data. By bringing them together with actual high frequency data, the project aims, in the long run, for a "grand unified theory" of finance with both theoretical and empirical components. As a corollary, this has the potential to induce transformational change by integrating risk management with business and regulatory decisions and data with models. This may help avoid some of the gravest model-with-no-data mistakes of the last few years. Methods of high frequency data also have application outside finance, such as in neural science and turbulence, and other areas where streaming data are available. Environmental science and monitoring also often present forms of high frequency data. Meanwhile, likelihood theory (which is central to this project) for time dependent data is a setting that connects finance and economics to a great variety of scientific endeavors, including biological and medical science, with mutual feedback between methods in these areas.