Date of Award

Spring 2022

Project Type


Program or Major


Degree Name

Doctor of Philosophy

First Advisor

Linyuan Li

Second Advisor

Ernst Linder

Third Advisor

Philip Ramsy


The Spline-based modeling has been an established tool for parametric and nonparametricregression modeling because of its continuous progress on theoretical and computational fronts over the last three decades. This thesis explores the idea of penalized spline modeling and goodness of fit testing in the context of time series testing in the frequency domain approach. The comparison of different time series is an important topic in statistical data analysis and has various applications in scientific research. One approach to identifying similarities or dissimilarities between two stationary processes is to compare the spectral densities of both time series. This thesis examines whether two stationary and independent time series with unequal lengths have the same spectral density. A new test statistic is proposed based on penalized splines regression. It relies on penalized splines estimator of an unspecified smooth function for the log-ratio of two spectral estimates, which are obtained from averaging out of the blocked periodograms for corresponding time series. Under the null hypothesis that two spectral densities are the same, the theoretical asymptotic distribution of the test statistic is derived. Several tests have been proposed in recent years: some of them are computationally intensive, and some lack stable size. Also, some current tests have low powers. So, we examined a relatively computationally fast and consistent test using penalized splines regression which reveals stable empirical type I error and good power properties. Simulation studies show that our proposed test is very comparable to the current test statistics in almost every case. Another advantage of our proposed test statistic is that it is very simple to construct and computationally fast based on a low-rank estimation technique.