Statistical Inferences And Applications For Two Classes Of Bivariate Integer-valued Threshold Autoregressive Models

Bivariate integer-valued time series data are widely used in various fields such as disease prevention and control,meteorological monitoring,and industrial injury insurance.Such data usually have characteristics such as nonlinearity and autocorrelation.Due to the particularity of data values,traditional continuous time series models cannot fit such data well.To solve the modeling problem of such data,this paper proposes two types of bivariate integer-valued threshold autoregressive models:Firstly,in order to describe the modeling problem of bivariate integer-valued time series data with nonlinear structure,a class of first-order bivariate integer-valued threshold autoregressive(BTINAR(1))models is proposed.Discuss the basic properties of this model,and on this basis,use the conditional least square method and conditional maximum likelihood method to estimate the parameters of the model,discuss the asymptotic properties of the estimator,and study the test of the existence of the threshold feature of the model problems,numerical simulations and empirical studies have been carried out.Empirical research shows that the established model is better than other similar models when fitting the sex crime data in Sydney,Australia,and can explain the data well.The above model can well describe the non-linear characteristics in bivariate integervalued time series,but there are also some shortcomings.For example,the diagonal case of the coefficient matrix is relatively limited,and the distribution of the innovation sequence is single.Therefore,in order to give a more general model,the BTINAR(1)model is extended,and a class of first-order full-coefficient bivariate integer-valued autoregressive(FBTINAR(1))process is proposed,and the innovation sequence Fundamental properties and parameter estimation problems of models following the bivariate Poisson and bivariate negative binomial distributions.Similar to the first part,the asymptotic properties of the estimated results are also discussed,and the problem of checking the threshold characteristics under the full coefficient model is studied.Finally,it is applied to a set of real data,and the empirical results show that the model fits better when there is cross-correlation to binary integer-valued time series data.