Date of Award

Fall 2025

Language

English

Embargo Period

11-17-2025

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, Michael Roy, Eric Rose

Keywords

Periodic Component, Variable Bandpass Periodic Block Bootstrap (VBPBB), Kolmogorov–Zurbenko Fourier Transform (KZFT), Missing Data, Imputation, Error

Subject Categories

Analysis | Applied Statistics | Biostatistics | COVID-19 | Environmental Monitoring | Longitudinal Data Analysis and Time Series | Other Environmental Sciences | Other Statistics and Probability | Statistical Methodology | Statistical Models | Statistical Theory

Abstract

Time series data are prevalent across a wide range of disciplines, including health surveillance, public policy, and environmental monitoring. In the presence of underlying cyclical patterns, the integrity of time series analysis depends critically on the ability to detect, model, and impute structured missing data without compromising the temporal structure. This dissertation introduces and validates a novel imputation framework that integrates the Variable Bandpass Periodic Block Bootstrap (VBPBB) into multiple imputation procedures, improving the accuracy, robustness, and interpretability of time series models under high rates of missingness and noise. The overarching goal of this dissertation was to develop and evaluate a periodicity-aware, structure-preserving methodology for time series imputation, and to demonstrate its practical utility through rigorous simulation studies and applications to real-world healthcare data. This purpose was operationalized through three interrelated objectives.

The first objective was to detect and quantify dominant periodic components in time series using VBPBB. This method builds on traditional block bootstrap techniques by filtering time series data through bandpass filters centered on specific frequencies, thereby isolating annual and harmonic components. Using New York State COVID-19 hospitalization data, this study demonstrated the superior capacity of VBPBB to generate narrow confidence intervals for periodic means, outperforming standard techniques and uncovering multiple significant harmonics of the annual cycle. The method provided strong evidence for stable, recurring seasonal components that traditional bootstrap approaches failed to detect, thus underscoring the relevance of advanced spectral techniques for healthcare data with latent seasonality.

The second objective was to incorporate these extracted periodic signals into a structure-aware imputation framework. By embedding the VBPBB-derived periodic covariates into the Amelia II multiple imputation engine, the framework preserved frequency-specific structure during the imputation process. Comparative simulations revealed that this VBPBB-enhanced imputation strategy consistently outperformed standard methods in both low- and high-noise environments, and across varying levels of missing data (5%–70%). Notably, the gains in performance were most pronounced under severe data loss and in the presence of complex, multicomponent signals. These findings validate the approach’s utility in contexts where both data completeness and structural fidelity are essential, such as pandemic surveillance and hospital capacity forecasting.

The third objective extended this evaluation by systematically simulating time series under three levels of signal complexity: annual only, annual with harmonics, and annual with harmonics plus monthly components, and applying both standard and VBPBB-enhanced imputation methods. Each scenario was tested across multiple levels of noise variance and missingness. Performance was measured using Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE), revealing that the VBPBB-based framework preserved both the mean and variance of the original signal more effectively than conventional approaches. In the most challenging conditions, 70% missingness with very high noise, VBPBB-based imputation maintained structural coherence and reduced error by up to 25% compared to standard models.

This dissertation also introduced several innovations with broad utility: a simulation-based protocol for validating time series imputation methods; a reproducible workflow for extracting significant periodic components using the KZFT and VBPBB methods; and a principled approach for integrating spectral information into time-domain imputation models. In practical terms, these tools offer a blueprint for improving data quality in healthcare systems where accurate monitoring and forecasting depend on structurally complete data. The tools and methods developed here are broadly applicable to public health, climate science, energy consumption forecasting, and other fields where periodic signals coexist with nonresponse or incomplete reporting.

The findings of this dissertation demonstrate that meaningful periodic structure in time series data can and should be leveraged to improve the quality of imputation and analysis. The integration of VBPBB with multiple imputation models not only enhances statistical validity but also strengthens the interpretability and operational utility of results. Future research should focus on extending this framework to multivariate settings, incorporating adaptive smoothing techniques, and embedding it within public health data pipelines for real-time applications. In doing so, this work lays the foundation for a new generation of imputation methods grounded in spectral awareness and methodological rigor.

License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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