Statistical Inference Of Copula-based Bivariate Random Coefficient Integer-valued Autoregressive Model

With the development of big data technology,the research on time series is getting deeper and deeper,and the research on integer-valued time series has also attracted extensive attention of scholars.The establishment of integervalued autoregressive models based on thinning operators is one of the classic methods to characterize integer-valued time series.The proposal of the binomial thinning operator lays the foundation for the integer-valued time series.From the univariate autoregressive model to the multivariate autoregressive model,the integer-valued autoregressive model is applicable for more fields.For the bivariate integer-valued autoregressive model,this paper mainly discusses two types of problems.One problem is to discuss the case where the thinning parameters are random.The Copula function is used to construct the distribution of the innovation term.The parameters of the model are estimated by the conditional least squares method and the conditional maximum likelihood method.At the same time,the numerical simulation method is used to compare the effects of the two estimation methods through the deviation and the mean square error.And finally an example analysis is carried out with the actual data,the results show that the marginal distribution is chosen as the negative binomial distribution,and the Copula function is chosen as the FGM Copula is more reasonable.Another kind of problem is that for the bivariate first-order integer autoregressive model,the Bayesian method is used to estimate the parameters of the model.When the innovation term follows a bivariate Poisson distribution,a Bayesian estimation framework is proposed,and numerical simulation is used to test the effect of Bayesian estimation method.