Statistical Inference For Binomial Autoregressive Processes With Dependent Thinning Operator

Integer-valued time series data is widely used in various scientific fields,especially in the fields of economics,sociology and insurance.This kind of data can be divided into two categories.One type is the observation data without a upper limit,such as the number of insurance claims of a company and the number of patients in a hospital.The other type is the finite-range time series data,such as the number of weekly rainy days in the Amazon rainforest or the number of states in German which have measles cases each month.This paper mainly studies the modeling and statistical inference of finite-range integer-valued time series data with dependent structure and zero inflation.The main content consists of three parts.In the first part,we propose a class of first-order binomial autoregressive(ADCBAR(1))model with alternative dependent thinning operator.The stationarity and ergodicity of model and the corresponding probabilistic and statistical properties are discussed in this part.The conditional least squares and conditional maximum likelihood methods are used to estimate the unknown parameters in ADCBAR(1)model and the asymptotic properties of the parameter estimators are studied.Finally,we apply the ADCBAR(1)model to the voting data of the Monetary Policy Council of the National Bank of Poland to show the advantages of our model.However,considering the transition coefficients between states may be affected by many factors and change with time.In the second part we consider the random coefficient extension of the ADCBAR(1)model.The probabilistic and statistical properties of the model,the unknown parameter estimation and the related numerical simulation research are discussed in this section.Finally,a real data example is used to demonstrate the necessity of the random coefficient extension of ADCBAR(1)model.In some situations,random coefficients may be influenced by some covariates.In order to describe the intrinsic structural characteristics of data accurately,the Logistic structure is introduced into the random coefficient ADCBAR(1)model in this paper.A covariate-driven first-order dependent binomial autoregressive model is proposed,and some probabilistic and statistical properties of the model are studied.For the unknown parameters in this model,we consider the conditional least squares and conditional maximum likelihood methods to estimate the parameters and study the corresponding limiting properties of estimators.Through the above research,we find that the ADCBAR(1)model and its extended model,established by introducing the alternative dependent thinning operator into the BAR(1)model,can well fit the integer-valued time series data with zero stacking feature and individual dependency in a limited range.