The Study And Application Of The Po-RCMTINAR(1) Model Under Poisson’s Innovation Sequence

In real life,integer-valued time series data is very common.It is an integer counting data formed by the state of a statistical indicator of a certain phenomenon at different times.Such data are widely used in many fields,such as communication security,health care,law,actuarial insurance,etc.The research of such data is also particularly important.Many scholars have also proposed different integer-valued time series models to study such data.The first-order mixed thinning inter-valued autoregressive model with fixed parameters is no longer realistic.Based on the existing integer-valued autoregressive models,this paper sets the original fixed thinning parameter in the integer-valued autoregressive model as random,and assumes that the random sequence in the model follows the Poisson distribution.Statistical properties and parameter estimation are studied based on the model.The main contents and conclusions are as follows:The newly defined model Po-RCMTINAR(1)is briefly analyzed and statistically inferred to obtain the statistical properties of the model.Three estimation methods are used to estimate the unknown parameters of model Po-RCMTINAR(1):(I)the Yule-Walker estimation of the unknown parameters of the model is solved.Based on this estimation method,the model is empirically analyzed and compared with other time series models.It is obtained that when analyzing the same set of actual data,the MSE value of model Po-RCMTINAR(1)is lower than that of other model,so model Po-RCMTINAR(1)has its advantages compared with other model;(II)the conditional least squares estimation of model parameters is solved and the asymptotic distribution of parameter estimation is established;(III)the conditional maximum likelihood estimation of model parameters is solved.According to the conditional least squares estimation and conditional maximum likelihood estimation of model Po-RCMTINAR(1),simulation studies are carried out and the advantages and disadvantages of these two methods are compared.It is concluded that under different sample sizes and parameter settings,the MADE and MSE values obtained by the conditional maximum likelihood estimation method are generally small,so the conditional maximum likelihood estimation method has superiority in the model Po-RCMTINAR(1).