DOI

10.17077/etd.btkr5v7t

Document Type

Dissertation

Date of Degree

Fall 2015

Degree Name

PhD (Doctor of Philosophy)

Degree In

Biostatistics

First Advisor

Cavanaugh, Joseph

First Committee Member

Foster, Eric

Second Committee Member

Oleson, Jacob

Third Committee Member

Polgreen, Philip

Fourth Committee Member

Zamba, Gideon

Abstract

This manuscript consists of two papers that formulate novel methodologies pertaining to time series analysis in the state-space framework.

In Chapter 1, we introduce an innovative time series forecasting procedure that relies on model-based clustering and model averaging. The clustering algorithm employs a state-space model comprised of three latent structures: a long-term trend component; a seasonal component, to capture recurring global patterns; and an anomaly component, to reflect local perturbations. A two-step clustering algorithm is applied to identify series that are both globally and locally correlated, based on the corresponding smoothed latent structures. For each series in a particular cluster, a set of forecasting models is fit, using covariate series from the same cluster. To fully utilize the cluster information and to improve forecasting for a series of interest, multi-model averaging is employed. We illustrate the proposed technique in an application that involves a collection of monthly disease incidence series.

In Chapter 2, to effectively characterize a count time series that arises from a zero-inflated binomial (ZIB) distribution, we propose two classes of statistical models: a class of observation-driven ZIB (ODZIB) models, and a class of parameter-driven ZIB (PDZIB) models. The ODZIB model is formulated in the partial likelihood framework. Common iterative algorithms (Newton-Raphson, Fisher Scoring, and Expectation Maximization) can be used to obtain the maximum partial likelihood estimators (MPLEs). The PDZIB model is formulated in the state-space framework. For parameter estimation, we devise a Monte Carlo Expectation Maximization (MCEM) algorithm, using particle methods to approximate the intractable conditional expectations in the E-step of the algorithm. We investigate the efficacy of the proposed methodology in a simulation study, and illustrate its utility in a practical application pertaining to disease coding.

Keywords

Forecasting, Model averaging, Particle methods, State-space modeling, Time Series Clustering, Zero-inflated binomial time series

Pages

xii, 80 pages

Bibliography

Includes bibliographical references (pages 76-80).

Copyright

Copyright © 2015 Fan Tang

Included in

Biostatistics Commons

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