Specification Analysis of Continuous-Time Models

连续时间模型的规范分析

• 批准号: 0850533
• 负责人: Yacine Ait-Sahalia
• 金额: $ 23.23万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0850533&HistoricalAwards=false
• 关键词: Specification; Analysis; Continuous; Time; Models

The objective of this proposal is to develop a range of specification tools for continuous-time models sampled at high frequency. Continuous-time stochastic processes known as semimartingales are effectively, up to technical conditions, the largest class of models that can be used to represent asset prices while still precluding arbitrage opportunities. As a result, they form the foundation of most theoretical asset pricing models. While these models have been widely studied in the probability literature, relatively few econometric and statistical procedures exist to determine the relative importance of different components of the model, test for their very presence, or look into some of their finer characteristics, such as the degree of activity of jumps.Semimartingales have different components: a possibly stochastic drift, a continuous martingale part which is the integral of a possibly stochastic volatility process with respect to a Brownian motion, and jumps, with a possibly stochastic Lévy measure. Ultimately, the objective of this proposal is to develop a nearly complete menu of specification tools for discretely-sampled semimartingales, and apply them on high frequency data:_ Which component(s) of the model should be included, given that some other components are already present;_ Which component(s) of the model can be distinguished from which existing components, and under whatrestrictions on the nature of the component(s);_ What are some of the finer characteristics of the jump components, such as the degree of activity of jumps, whether they have finite or infinite activity, etc.Broader Impacts: While many of the examples and motivation for the work that are described in this proposal come from economics and finance, this proposal is fundamentally about developing methodologies that are applicable to generic semimartingales. Semimartingales are some of the most common tools from probability used to model stochastic processes. One can hope that some of the econometric and statistical methods developed here can find applications in physics, engineering or seismology, which are all fields where observations are also available at very high frequencies.The project integrates research and education by working closely with students and funding them in the form of summer research assistantships, creating datasets and developing publicly available computer code (both made available through the web, as has been the case for past projects) for each of the main research endeavors funded by this proposal. Various research findings and examples will be simplified and taught in both undergraduate and graduate courses. In particular, they will be used in supervising undergraduate senior theses and Ph.D. theses. Postdoctoral fellows and underrepresented groups will be trained as a part of the research covered by this proposal. The results will be disseminated broadly through presentations at seminars, conferences and professional association meetings.Finally, this project involves collaborations with colleagues in different disciplines (economics, statistics, probability) and academic institutions in the U.S. (Per Mykland, a statistician at the University of Chicago, Joon Park, an economist at Texas A&M University, Lan Zhang, a statistician at UIC) and abroad (Jean Jacod, a probabilist at Université Paris VI).

本提案的目的是为高频采样的连续时间模型开发一系列规范工具。在技术条件下，连续时间随机过程被称为半鞅，是可用于表示资产价格同时仍排除套利机会的最大类模型。因此，它们构成了大多数理论资产定价模型的基础。虽然这些模型已经在概率文献中得到了广泛的研究，但相对较少的计量经济学和统计学程序存在，以确定模型的不同组成部分的相对重要性，测试它们的存在，或研究它们的一些更精细的特征，如跳跃的活动程度。半鞅有不同的组成部分：一个可能的随机漂移，一个连续的鞅部分，这是一个可能的随机波动过程的积分布朗运动，跳跃，与可能的随机Lévy措施。最后，本提案的目标是为离散抽样半鞅开发一套几乎完整的规范工具，并将其应用于高频数据：--在已经存在某些其他组成部分的情况下，模型的哪些组成部分应该包括在内;--模型的哪些组成部分可以与哪些现有组成部分区分开来，以及在哪些条件下对组成部分的性质加以限制;- 跳跃成分的一些更精细的特征是什么，例如跳跃的活动程度，它们是否具有有限或无限的活动，等等。更广泛的影响：虽然本提案中描述的许多例子和工作动机来自经济和金融，这个建议基本上是关于发展适用于一般半鞅的方法。半鞅是概率论中用来模拟随机过程的最常见的工具。我们希望这里开发的一些计量经济学和统计方法可以在物理学、工程学或地震学中找到应用，这些领域也可以进行非常高频率的观测。该项目通过与学生密切合作并以夏季研究助学金的形式资助他们，将研究和教育结合起来，为本提案资助的每一项主要研究工作创建数据集并开发可公开获取的计算机代码（与过去的项目一样，都可通过网络获取）。各种研究结果和例子将被简化，并在本科和研究生课程中教授。特别是用于指导本科生、高级学位论文和博士学位论文。论文博士后研究员和代表性不足的群体将接受培训，作为本提案所涉研究的一部分。最后，本项目还与美国（芝加哥大学统计学家Per Mykland、德克萨斯农工大学经济学家Joon Park、UIC统计学家张兰）和国外（巴黎第六大学概率学家Jean Jacod）的不同学科（经济学、统计学、概率学）和学术机构的同事进行了合作。