Theses and Dissertations

Nusrat Jahan

Issuing Body

Mississippi State University

Advisor

Harvill, Jane L.

Committee Member

Jonkman, Jeffery

Committee Member

Picone, Joseph

Committee Member

Gerard, Patrick

Committee Member

Oppenheimer, Seth

Date of Degree

8-5-2006

Document Type

Dissertation - Open Access

Major

Mathematical Sciences

Degree Name

Doctor of Philosophy

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

Abstract

In this study, we present two new frequency domain tests for testing the Gaussianity and linearity of a sixth-order stationary univariate time series. Both are two-stage tests. The first stage is a test for the Gaussianity of the series. Under Gaussianity, the estimated normalized bispectrum has an asymptotic chi-square distribution with two degrees of freedom. If Gaussianity is rejected, the test proceeds to the second stage, which tests for linearity. Under linearity, with non-Gaussian errors, the estimated normalized bispectrum has an asymptotic non-central chi-square distribution with two degrees of freedom and constant noncentrality parameter. If the process is nonlinear, the noncentrality parameter is nonconstant. At each stage, empirical distribution function (EDF) goodness-ofit (GOF) techniques are applied to the estimated normalized bispectrum by comparing the empirical CDF with the appropriate null asymptotic distribution. The two specific methods investigated are the Anderson-Darling and Cramer-von Mises tests. Under Gaussianity, the distribution is completely specified, and application is straight forward. However, if Gaussianity is rejected, the proposed application of the EDF tests involves a transformation to normality. The performance of the tests and a comparison of the EDF tests to existing time and frequency domain tests are investigated under a variety of circumstances through simulation. For illustration, the tests are applied to a number of data sets popular in the time series literature.

URI

https://hdl.handle.net/11668/17333

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