Estimation and Inference Methods for Continuous-Time Models

这一研究项目涉及为高频采样的连续时间半鞅模型开发新的估计和推断工具。半鞅模型是最一般的资产价格模型，它排除了套利机会，因此成为现代资产定价中的主力模型。半鞅模型有不同的组成部分：捕捉资产价格平稳运动的随机漂移，模拟扩散波动的连续鞅部分，以及捕捉资产价格突变的跳跃部分。虽然每个组件在应用程序中扮演着不同的角色，但从统计上讲，将一个组件从其他组件中分离出来并不是一件微不足道的事情。本项目的目标是开发一种新的半鞅跳跃分量的统计估计和推断方法。与现有的方法相比，新的方法将更加稳健，特别是当价格跳跃很难从数据中识别时。虽然拟议活动中的激励例子是金融模型的例子，但本项目中开发的方法对于一般半鞅是有效的。半鞅在随机过程和随机微积分的一般理论中起着核心作用。除经济和金融外，半鞅还被应用于生物、化学和电子领域。这里开发的计量经济学和统计学方法可以在这些领域找到应用，只要有高频观测。该项目通过与研究生以研究助学金的形式密切合作，将研究和教育结合在一起。拟议的方法涉及新的实施程序，其代码将公开提供。结果将通过出版物和在研讨会、会议和专业协会会议上的陈述广泛传播。

This research project involves developing new estimation and inference tools for continuous-time semimartingale models sampled at high frequency. The semimartingale model is the most general model for asset prices that precludes arbitrage opportunities and, as a result, has been the workhorse model in modern asset pricing.Semimartingales have different components: a stochastic drift capturing the smooth movement of the asset price, a continuous martingale part modeling diffusive volatility and a jump part capturing abrupt movements of the asset price. While each component plays a distinct role in applications, it is statistically nontrivial to disentangle one component from the others. The objective of this project is to develop a novel statistical estimation and inference procedure for the jump component of the semimartingale. Compared with the existing methods, the new procedure will be more robust, especially when price jumps are difficult to identify from the data.While the motivating examples in the proposed activity are those of financial models, the methods developed in this project are valid for generic semimartingales. Semimartingales play a central role in the general theory of stochastic processes and stochastic calculus. Besides economics and finance, semimartingales have also been used in biological, chemical, and electrical applications. The econometric and statistical methods developed here may find applications in these fields provided that observations are available at high frequencies.The project integrates research and education by working closely with graduate students in the form of research assistantships. The proposed methodologies involve new implementation procedures whose code will be made publicly available. The results will be disseminated broadly through publications and presentations at seminars, conferences and professional association meetings.