A Study on Mixture Poisson Autoregressive (P) Model

Abstract

This research presents and assesses novel models for time series count data called the Mixture Poisson Autoregressive (MPAR) model addresses difficulties of discreteness, overdispersion, and serial correlation. A completely parametric technique was used, and a marginal distribution for the counts was defined. The parameters of the model were estimated using the Expectation Maximization method, through extensive Monte Carlo simulations, the stability of the estimates of the MPAR was evaluated and the results clearly revealed that the model was stable as the estimated parameters were converging to the values of the true parameters as the sample gets larger. Also, the results from the simulations revealed that the MPAR model outperform other count data models thus, Poisson distribution, Poisson Autoregressive (PAR) and Poisson Exponentially Weighted Moving Average (PEWMA).