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首页> 外文期刊>Journal of Time Series Analysis >CONWAY-MAXWELL-POISSON AUTOREGRESSIVE MOVING AVERAGE MODEL FOR EQUIDISPERSED, UNDERDISPERSED, AND OVERDISPERSED COUNT DATA
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CONWAY-MAXWELL-POISSON AUTOREGRESSIVE MOVING AVERAGE MODEL FOR EQUIDISPERSED, UNDERDISPERSED, AND OVERDISPERSED COUNT DATA

机译：Conway-Maxwell-Poisson自动进球移动平均模型，用于等偏见，欠分支和过度分散的计数数据

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摘要

In this work, we propose a dynamic regression model based on the Conway & x16e;Maxwell-Poisson (CMP) distribution with time-varying conditional mean depending on covariates and lagged observations. This new class of Conway & x16e;Maxwell-Poisson autoregressive moving average (CMP-ARMA) models is suitable for the analysis of time series of counts. The CMP distribution is a two-parameter generalization of the Poisson distribution that allows the modeling of underdispersed, equidispersed, and overdispersed data. Our main contribution is to combine this dispersion flexibility with the inclusion of lagged terms to model the conditional mean response, inducing an autocorrelation structure, usually relevant in time series. We present the conditional maximum likelihood estimation, hypothesis testing inference, diagnostic analysis, and forecasting along with their asymptotic properties. In particular, we provide closed-form expressions for the conditional score vector and conditional Fisher information matrix. We conduct a Monte Carlo experiment to evaluate the performance of the estimators in finite sample sizes. Finally, we illustrate the usefulness of the proposed model by exploring two empirical applications.
机译：在这项工作中，我们提出了一种基于Conware＆X16E的动态回归模型; Maxwell-Poisson（CMP）分布，根据协变量和滞后观察，具有时变条件平均值。这类新一类Conway＆X16e; Maxwell-Poisson自动增加移动平均（CMP-ARMA）模型适用于分析时间序列的计数。 CMP分布是泊松分布的双参数概括，允许建模已解雇，等异点和过量数据。我们的主要贡献是将这种色散灵活性与包含滞后的术语相结合，以模拟条件平均反应，诱导自相关结构，通常在时间序列中相关。我们介绍了条件最大似然估计，假设检测推断，诊断分析和预测及其渐近性质。特别是，我们为条件分数矢量和条件Fisher信息矩阵提供闭合表达式。我们进行蒙特卡罗实验，以评估估算器在有限样本尺寸中的性能。最后，我们通过探索两个实证应用来说明所提出的模型的有用性。

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