Date of Award

Spring 2026

Language

English

Embargo Period

4-16-2026

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Epidemiology and Biostatistics

Program

Biostatistics

First Advisor

Edward Valachovic

Committee Members

Edward Valachovic, Eric Rose, Kai Zhang

Keywords

VBPBB, Time Series, Periodic Mean Bias, Cross Validation, ROCV

Subject Categories

Applied Statistics | Biostatistics | Environmental Health and Protection

Abstract

Time series analysis is essential for understanding long-term patterns, periodic behavior, and underlying correlations in complex datasets. The periodically correlated (PC) time series is a type of time series where the correlation structure repeats over fixed intervals. The Variable Bandpass Periodic Block Bootstrap (VBPBB) has recently been proposed as a resampling method that preserves PC structures through the use of periodogram, bandpass filters, and block bootstrap resampling. Although promising, VBPBB remains underutilized, and its limitations have not been fully examined. This dissertation advances both the application and methodological development of the VBPBB.

The first project applies the VBPBB to a modeled 16-year dataset of daily mean PM2.5 concentrations collected in Manhattan, New York. This analysis demonstrates the ability of VBPBB to identify semi-annual, tri-annual, and weekly periodic components that are not detected by conventional block bootstrap approaches, providing new insights into the temporal dynamics of PM2.5, a pollutant of central concern in environmental health.

The second project investigates potential bias in VBPBB, motivated by its reliance on block bootstrap methodology. We introduce and evaluate several new concepts—overall mean bias, pointwise mean bias, and periodic mean bias—to quantify and understand bias in this framework. These concepts not only clarify the properties of VBPBB but may also be applied in broader bootstrap contexts across different research domains.

The final project addresses the long-standing challenge of selecting optimal arguments for the Kolmogorov-Zurbenko Fourier Transform (KZFT) filters used within VBPBB. This dissertation develops a cross-validation framework that enables data-driven determination of filter arguments, built upon the bias analysis in the second project.

In addition to the three projects above, I added an extra chapter that applies the method from the third project to validate the real-world data used in the first project.

Together, these contributions extend the methodological robustness of the VBPBB, demonstrate its practical utility in environmental applications, and provide tools and frameworks that enhance its accessibility for future researchers.

License

This work is licensed under the University at Albany Standard Author Agreement.

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