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.

这项工作提出了一类新的模型，即 Conway-Maxwell-Poisson 季节性自回归移动平均模型 (CMP-SARMA)，它通过将季节性成分包含到动态模型结构中来扩展 Conway-Maxwell-Poisson 自回归移动平均模型的类别。建议的模型类别假设响应变量为 Conway-Maxwell-Poisson 条件分布，这使我们能够对具有过度分散、等分散和欠分散的非负计数的单变量时间序列进行建模。我们通过条件最大似然估计参数。我们还提供了条件评分函数和条件 Fisher 信息矩阵的封闭式表达式。此外，还提出了假设检验、诊断分析和预测，并讨论了渐近结果。进行蒙特卡罗模拟研究以评估估计量的有限样本特性。最后，我们将新模型应用于实际数据，并将结果与​​文献中的其他模型进行比较。