A Mixed Time Series Model of Binomial Counts

Continuous time series modelling has been an active research in the past few decades. However, time series data in terms of correlated counts appear in many situations such as the counts of rainy days and access downloading. Therefore, the study on count data has become popular in time series modelling recently. This article introduces a new mixture model, which is an univariate non-negative stationary time series model with binomial marginal distribution, arising from the combination of the well-known binomial thinning and Pegram's operators. A brief review of important properties will be carried out and the EM algorithm is applied in parameter estimation. A numerical study is presented to show the performance of the model. Finally, a potential real application will be presented to illustrate the advantage of the new mixture model.