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.
In this project, several statistical methods have been developed for disentangling and modeling two types of fluctuations, that is, diffusive movements and jumps, for a general class of semimartingale models. The semimartingale model is broadly used in financial applications such as risk management, and is also widely used in biological, chemical, and electrical applications. Several research papers that are listed below have been (partially) supported by this project. These research papers are available to the general public and have been discussed in several conference and seminar presentations. The first main finding of this project concerns the jump-type movements. While jumps are prevalent in financial data and, hence, exhibit an important source of risk, it is found that precisely measuring their magnitude is statistically difficult. A new method is developed for conducting valid statistical inference even in "singular" settings in which existing methods in the literature fail to work. A statistical method for evaluating forecast models for jumps is also developed. The second main finding of this project concerns the diffusive movements. The magnitude of such movements is measured by volatility. The project provides a method that allows one to measure volatility with minimal assumptions. Volatility plays an important role in risk management, economic modeling and financial forecasting. Statistical methods are also developed for these specific applications. Publications: Robust Estimation and Inference for Jumps in Noisy High Frequency Data: a Local-to-Continuity Theory for the Pre-averaging Method. Econometrica, 81, 1673-1693, 2013. Volatility Occupation Times (with G. Tauchen and V. Todorov), 41,1865-1891, 2013, Annals of Statistics.
