Count data time series models and their applications

“Due to fast developments of advanced sensors, count data sets have become ubiquitous in many fields. Modeling and forecasting such time series have generated great interest. Modeling can shed light on the behavior of the count series and to see how they are related to other factors such as the environmental conditions under which the data are generated. In this research, three approaches to modeling such count data are proposed. First, a periodic autoregressive conditional Poisson (PACP) model is proposed as a natural generalization of the autoregressive conditional Poisson (ACP) model. By allowing for cyclical variations in the parameters of the model, it provides a way to explain the periodicity inherent in many count data series. For example, in epidemiology the prevalence of a disease may depend on the season. The autoregressive conditional Poisson hidden Markov model (ACP-HMM) is developed to deal with count data time series whose mean, conditional on the past, is a function of previous observations, with this relationship possibly determined by an unobserved process that switches its state or regime as time progresses. This model, in a sense, is the combination of the discrete version of the autoregressive conditional heteroscedastic (ARCH) formulation and the Poisson hidden Markov model. Both the above models address the frequently present serial correlation and the clustering of high or low counts observed in time series of count data, while at the same time allowing the underlying data generating mechanism to change cyclically or according to a hidden Markov process. Applications to empirical data sets show that these models provide a better fit than the standard ACP models. In addition to the above models, a modification of a zero-inflated Poisson model is used to analyze activity counts of the fruit fly. The model captures the dynamic structure of activity patterns and the fly\u27s propensity to sleep. The obtained results when fed to a convolutional neural network provides the possibility of building a predictive model to identify fruit flies with short and long lifespans”--Abstract, page iv