A new model for time series of counts

Abstract

Time series modelling is an active research area in the past few decades with much attention focused in the continuous setting. However, time series data in terms of correlated counts occur in many situations. Thus modelling of time series of count data has attracted the attention many researchers recently. A new univariate non-negative stationary time series model of count data is introduced and is referred to as the mixture of Pegram and thinning on first order integer-valued autoregressive (MPT(1)) process. It is constructed from the combination of the popular thinning and Pegram's operators. The motivation for introducing the model and important statistical properties are discussed, such as autocorrelation, regression and joint distribution. Some simulation results are presented to show the performance of the model. Finally, the advantage of this new model is illustrated with application to a real data set.