ORCID
https://orcid.org/0000-0001-5243-3092
Date of Award
Spring 2025
Language
English
Embargo Period
4-28-2025
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
College/School/Department
Department of Epidemiology and Biostatistics
Program
Biostatistics
First Advisor
Igor Zurbenko
Committee Members
Edward Valachovic, Mingzeng Sun
Keywords
Time series analysis, Kolmogorov-Zurbenko periodograms, DiRienzo-Zurbenko algorithm smoothing, Neagu-Zurbenko algorithm smoothing, Signal frequency and strength estimates, Climate change and coastal water level
Abstract
The purpose of this Dissertation was to establish the theoretical and practical limits of Kolmogorov-Zurbenko periodograms with dynamic smoothing in contrast to standard periodograms with static smoothing, along with a practical application of Kolmogorov-Zurbenko time series analysis methods. It was determined that Kolmogorov-Zurbenko periodograms with dynamic smoothing were superior to standard periodograms with static smoothing in estimating signal frequencies with respect to sensitivity, accuracy, and resolution, and that they are robust in the face of missing data. However, their precision in estimating signal strength exceeds that of standard periodograms with static smoothing in only the most extreme circumstances and, thus, precision is conditional. In a practical application assessing the impact of climate change on coastal water levels for Virginia Key, Florida, a full complement of Kolmogorov-Zurbenko time series analysis methods found total water levels could rise as high as 4.18 feet between 1994 and 2050 using a linear model and could rise as high as 8.07 feet over the same time period using a quadratic model; given their magnitude, these findings have implications for both emergency preparedness and governmental policies. This Dissertation also led to a set of innovative developments including identification of criteria to systematically evaluate periodograms and their smoothing algorithms, formulation of a new protocol for conducting spectral analysis, and construction of a methodological template to study changes in coastal water levels associated with climate change.
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Loneck, Barry M., "The Theoretical and Practical Limits of Kolmogorov-Zurbenko Periodograms with Dynamic Smoothing in the Spectral Analysis of Time Series Data" (2025). Electronic Theses & Dissertations (2024 - present). 141.
https://scholarsarchive.library.albany.edu/etd/141
