Date of Award

Spring 2023

Project Type


Program or Major


Degree Name

Doctor of Philosophy

First Advisor

Linyuan Li

Second Advisor

Qi Zhang

Third Advisor

Rita Hibschweiler


The goodness-of-fit tests for time series models have been discussed for years. Most of the current goodness-of-fit tests require the calculation of residuals from the fitted model. Such calculations can be tedious, and in some cases, the tests are even unreliable. Furthermore, most of their results require assumptions that rule out long memory processes, whose autocorrelation decays at a hyperbolic rate as the lag increases and has become popular in time series modeling. In this thesis, a new goodness-of-fit test for time series data is proposed. The test statistic is based on the ratio between the periodogram and the parametric spectral density or its estimator under the null. The asymptotic distribution of the proposed test statistic is derived and its power properties are discussed. Unlike most current goodness-of-fit tests, the asymptotic distribution of our test statistic allows the null hypothesis to be either a short- or long-range dependence model. As our test is in the frequency domain, it is easy to compute, and it does not require the calculation of residuals from the fitted model. The finite sample performance of the test is investigated through simulation experiments.