基于Katz分布的计数数据自回归模型以及其在预测呼吸系统患病人数中的应用

Integer Valued Autoegressive Process with Katz Arrivals and Its Application in Predicting the Count of the Cases of Respiratory Disease

泊松自回归模型假设到达过程为期望与方差相等的泊松分布,但事实上真正的数据生成过程中的到达过程的方差既可以高于期望也可以低于期望.本文提出了基于Katz到达过程(Katz arrivals)的计数数据自回归模型(INAR-Katz:integer valued autoregressive process with Katz arrivals).并采用蒙特卡罗模拟方法(Monte Carlo simulations)比较了INAR-Katz模型在矩估计以及极大似然估计下的估计准确程度.最后采用INAR-Katz模型对患呼吸系统疾病的急诊就诊人数进行建模,结果显示INAR-Katz模型优于普通泊松模型、PAR模型,具有很好的应用前景.

The traditional PAR process(Poisson autoregressive process)assumes that the arrival process is the equi-dispersed Poisson process,with its mean being equal to its variance.Whereas the arrival process in the real DGP(data generating process)could either be over-dispersed,with variance being greater than the mean,or under-dispersed,with variance being less than the mean.This paper proposes using the Katz family distributions to model the arrival process in the INAR process(integer valued autoregressive process with Katz arrivals)and deploying Monte Carlo simulations to examine the performance of maximum likelihood(ML)and method of moments(MM)estimators of INAR-Katz model.Finally,we used the INAR-Katz process to model count data of hospital emergency room visits for respiratory disease.The results show that the INAR-Katz model outperforms the Poisson model,PAR(1)model,and has great potential in empirical application.