First-Order Integer-Valued Moving Average Process with Power Series Innovations

Abstract

In this paper, we introduce a first-order nonnegative integer-valued moving average process with power series innovations based on a Poisson thinning operator (PINMAPS(1)) for modeling overdispersed, equidispersed and underdispersed count time series. This process contains the PINMA process with geometric, Bernoulli, Poisson, binomial, negative binomial and logarithmic innovations which some of them are studied in details. Some statistical properties of the process are obtained. The unknown parameters of the model are estimated using the Yule-Walker, conditional least squares and least squares feasible generalized methods. Also, the performance of estimators is evaluated using a simulation study. Finally, we apply the model to three real data set and show the ability of the model for predicting data compared to competing models.

Keywords

• First-order integer-valued moving average process
• Poisson thinning operator
• Moving average model
• Power series family of distributions