Title

A factor and vector-AR model on analyzing high dimension volatility for high-frequency financial data

Date of Completion

January 2007

Keywords

Statistics

Degree

Ph.D.

Abstract

In this dissertation, we take up one focus point in the study of high frequency finance, namely, to estimate the integrated volatility over a low frequency unit of time, usually a day, using intra-day high frequency data. There are already many existing methods available, and our major renovation would be to extend the usual realized volatility type of estimation of one or few assets to a large number of assets, usually in the magnitude of hundreds. Such increase in dimension poses extra challenge and we will propose a model that will perform the dimension reduction such that the statistical estimation will become feasible. ^ We will briefly introduce the relevant terms and concepts, as well as a general frame work for the realized volatility in sec 2.1. Sec 2.2 is the core of our development and we propose a new factor model for the realized volatility ma trices. We explain the ways to estimate the model and we also establish that our estimators are consistent under suitable conditions. After that, we explain how a conventional vector-AR model may be fitted to the low dimensional matrices. ^ We then in chapter 3 discuss the issue of practical implementation of the model. We will examine the available methods and use simulation to investigate whether some elementary methods will work well if we simulate from a well-defined structure that is contaminated with noise. ^ Finally we put the model to test using two large scale real market data sets in chapter 4. We will examine whether the model is really applicable to those real transaction data and how well the final time series model fits. ^