Detecting and Modelling Serial Dependence in Nongaussian and Nonlinear Time Series

Abstract

Discrete time series data is seen in a wide variety of disciplines including biology, medicine, psychology, criminology and economics. However, traditional methods of detecting serial correlation in time series are not specifically designed for detecting serial dependence in discrete-valued time series. Thus new methods are needed to provide informative and implementable testing approaches.This thesis is concerned with detection and estimation of serial dependence for a variety of observation-driven and parameter-driven models for regression analysis in binary and binomial time series. Generalised linear models (GLMs) are widely used for modelling discrete-valued data but do not allow for serial dependence and, as a result, inferences about regression effects may be invalid for time series application. Two classes of extended GLM have arisen to deal with this issue: observation-driven models and parameter-driven models, in which the serial dependence of the former relies on previous observations and residuals, and the serial dependence of the latter derives from an unobserved latent process. This thesis is structured in two parts corresponding to these two model classes. Chapter 1 provides a review of these models and existing methods for detecting and estimating serial dependence in them. Chapters 2 to 4 focus on observation-driven models and Chapters 5 to 7 focus on parameterdriven models. Chapter 8 distils the main results and conclusions from the thesis and suggests future research opportunities. The thesis proposes the use of score tests because they can be implemented using standard GLM fitting software or, for the parameter-driven models, software for fitting generalised linear mixed models, which is also readily available in most advanced statistical packages.