Date of Award

5-2001

Degree Type

Report

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Piotr Kokoszka

Second Advisor

Richard Cutler

Third Advisor

Russell Thompson

Abstract

The purpose of this paper is to examine and model data from several years of foreign currency trading, to determine if one or more change points has occured in the data, and to estimate when those change points took place. Leading up to the analysis of the data we will construct and develop several statistics which we will use to determine if a change point has occured.

This paper falls into the area of computational statistics and will make use of Splus and the S+GARCH module within Splus. Heavy use will also be made of C++. The models that we will be utilizing and discussing throughout the paper are the autoregressive conditional heteroscedasticity (ARCH) model and the generalized autoregressive conditional heteroscedasticity (GARCH) model. These specific models, along with several other similar models will be formally defined later in the paper.

With the GARCH module in Splus we are able not only to simulate ARCH and GARCH data , but also to estimate the parameters of these ARCH and GARCH models from the data. Naturally we are interested in the accuracy of these estimation techniques . If we are not able to accurately estimate the parameters of simulated ARCH and GARCH data, we can assume that we would likewise have difficulty in estimating parameters of data that is only proposed to follow these ARCH or G ARCH models.

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