Conway–Maxwell–Poisson seasonal autoregressive moving average model

Abstract

This work proposes a new class of models, namely Conway–Maxwell–Poisson seasonal autoregressive moving average model (CMP-SARMA), which extends the class of Conway–Maxwell–Poisson autoregressive moving average models by including seasonal components to the dynamic model structure. The proposed class of models assumes a Conway–Maxwell–Poisson conditional distribution for the response variable, which allows us to model univariate time series of non-negative counts with overdispersion, equidispersion, and underdispersion. We estimated the parameters by conditional maximum likelihood. We also present closed-form expressions for the conditional score function and conditional Fisher information matrix. In addition, hypothesis testing, diagnostic analysis, and forecasting are proposed and asymptotic results are discussed. A Monte Carlo simulation study is conducted to evaluate the finite sample properties of the estimators. Finally, we present an application of the new model to real data and compare the results with other models in the literature.