Modeling count time series following generalized linear models

Abstract

Count time series are found in many different applications, e.g. from medicine, finance or industry, and have received increasing attention in the last two decades. The class of count time series following generalized linear models is very flexible and can describe serial correlation in a parsimonious way. The conditional mean of the observed process is linked to its past values, to past observations and to potential covariate effects. In this thesis we give a comprehensive formulation of this model class. We consider models with the identity and with the logarithmic link function. The conditional distribution can be Poisson or Negative Binomial. An important special case of this class is the so-called INGARCH model and its log-linear extension. A key contribution of this thesis is the R package tscount which provides likelihood-based estimation methods for analysis and modeling of count time series based on generalized linear models. The package includes methods for model fitting and assessment, prediction and intervention analysis. This thesis summarizes the theoretical background of these methods. It gives details on the implementation of the package and provides simulation results for models which have not been studied theoretically before. The usage of the package is illustrated by two data examples. Additionally, we provide a review of R packages which can be used for count time series analysis. A detailed comparison of tscount to those packages demonstrates that tscount is an important contribution which extends and complements existing software. A thematic focus of this thesis is the treatment of all kinds of unusual effects influencing the ordinary pattern of the data. This includes structural changes and different forms of outliers one is faced with in many time series. Our first study on this topic is concerned with retrospective detection of such changes. We analyze different approaches for modeling such intervention effects in count time series based on INGARCH models. Other authors treated a model where an intervention affects the non-observable underlying mean process at the time point of its occurrence and additionally the whole process thereafter via its dynamics. As an alternative, we consider a model where an intervention directly affects