Date of Award

Spring 2026

Language

English

Embargo Period

4-23-2026

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

Eric Rose, Valarie Haley

Keywords

non parametric, time series, periodic principal components, Variable Band Pass Block Bootstrap

Subject Categories

Biostatistics

Abstract

This dissertation investigates methods for mean estimation in periodically correlated time series, focusing on the Variable Bandpass Periodic Block Bootstrap (VBPBB) and a novel data-driven maxima method. Time series require specific methods because of the temporal correlation in the data. Traditional methods like the General Seasonal Block Bootstrap (GSBB) account for this correlation but often produce wide confidence intervals because they cannot isolate multiple periodicities, allowing noise and other frequencies to interfere with analysis. The VBPBB method addresses this by applying a Kolmogorov-Zurbenko Fourier Transform (KZFT) filter to the data before bootstrapping, which suppresses interfering frequencies and results in narrower, more precise confidence bands.

Practical application of the VBPBB method to an analysis of nitrogen dioxide (NO2) levels in Los Angeles demonstrates its efficacy. The method identified a significant annual periodic component that was obscured when using the GSBB method due to its wider confidence intervals. To move beyond relying on theoretical assumptions for selecting frequencies, this work introduces the maxima method, an algorithm that identifies potential principal periodic components directly from the data. This technique involves smoothing a periodogram to identify local maxima, defining analysis windows by observing changes in slope, and then testing the highest amplitude frequencies within those windows for significance using the VBPBB method.

In simulations, the maxima method proved highly robust, correctly identifying principal periodic components and their harmonics across low, medium, and high frequencies. It maintained high accuracy even at signal-to-noise ratios as low as 1:50, correctly identifying components in 30 out of 30 trials in most scenarios. When applied back to the Los Angeles NO2 dataset, the maxima method successfully identified significant daily and 12-hour harmonic components that were consistent with expected urban commuting patterns. While the method can identify false positives or long-term trends that are impossible to analyze given the limitations of the data set’s length, it serves as a powerful complement to theoretical analysis, particularly when underlying periodic mechanisms are not fully understood. Integrating the maxima method with VBPBB allows for a more rigorous analysis of multiple periodicities in complex time series data.

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