Estimation and Inference Methods for Continuous-Time Models

本研究项目涉及为高频采样的连续半鞅模型开发新的估计和推理工具。半鞅模型是最通用的资产价格模型，它排除了套利机会，因此一直是现代资产定价的主力模型。半鞅有不同的组成部分：捕获资产价格平滑运动的随机漂移，建模扩散波动的连续鞅部分和捕获资产价格突然运动的跳跃部分。虽然每个组件在应用程序中都扮演着不同的角色，但从统计学上讲，将一个组件与其他组件区分开来是很重要的。本课题的目标是开发一种新的半鞅跳跃分量的统计估计和推理程序。与现有方法相比，新程序将更加稳健，特别是当价格跳跃难以从数据中识别时。虽然在提议的活动中激励的例子是那些金融模型，在这个项目中开发的方法是有效的一般半鞅。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。除了经济和金融，半马丁还被用于生物、化学和电气领域。这里发展的计量经济学和统计方法可以在这些领域中找到应用，只要在高频率上可以观测到。该项目将研究与教育结合起来，以研究助教的形式与研究生密切合作。拟议的方法涉及新的实现程序，其代码将公开提供。研究结果将通过出版物和在研讨会、会议和专业协会会议上的演讲广泛传播。

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.