Structural time series clustering, modeling, and forecasting in the state-space framework

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 parameterdriven 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. iv PUBLIC ABSTRACT Time series forecasting is an important practical problem. By incorporating information from series that exhibit similar long-term and transitory behaviors, we can potentially improve the forecasting accuracy for a particular series of interest. However, identifying and appropriately utilizing a cluster of related series from a larger pool presents a daunting challenge. The first paper in this thesis introduces a time-series forecasting procedure that relies on model-based clustering and model averaging. The proposed technique is applied to a collection of monthly disease incidence series. Our approach yields both clinically and statistically meaningful clusters, and through model averaging, yields more accurate forecasts than those produced by any individual model. The second paper proposes a general methodology to model count time series with excess zeros. This type of data is commonly encountered in many biomedical and public health applications. In hospital epidemiology, for example, the incidence for a rare nosocomial infectious disease could be predominantly zero, yet feature positive counts when there is an outbreak. In occupational health, the number of injuries for hospital workers might exhibit a similar behavior. Our objective is to develop novel modeling frameworks to describe count time series with a preponderance of zeros, where the counts arise based on a predetermined number of binary trials. To fulfill this objective, we propose two general classes of models. We investigate the efficacy of the proposed methodology in a simulation study, and illustrate its utility in a practical application pertaining to disease coding.