INAR Model Based On Poisson-BE2 Innovations

Integer-valued time series data refers to counting data formed by a certain phenomenon in different states in a period of time.which widely exists in all areas of social production and social living,such as the number of alarms about a certain crime per month,the number of patients visiting a hospital within per week,and the number of shares traded per month,and so on.These data often have the characteristics of over dispersion.Therefore,modeling and analyzing of such data have attracted widely attention and research by scholars.In recent,many studies are based on the situation of describing overdispersed data.and integer-valued time series models for such data start form the integer-valued autoregressive model based on binomial thinning operator in the 1980 s,After that,scholars studied a series of problems of the model.To analyze different types of integer-valued time series data,scholars continue to promote and generalize integer-valued time series models,such as integer-valued autoregressive model with Poisson innovations,integer-valued autoregressive model with compound Poisson innovations,integer value autoregressive model with geometric innovations,integer-valued autoregressive model with negative binomial innovations,integer-valued autoregressive models with Poisson-Lindley innovations and so on.Once these models appear,they have received extensively attention and research from scholars,and were widely applied to process equi-dispersed and over-dispersed integer-valued time series data.This paper proposes a new class of integer-valued autoregressive models based on Poisson binomial-exponential 2 distribution of two parameters(denoted as PBE2)and binomial thinning operator,Here PBE2 is obtained by mixing the Poisson distribution and the two-parameter binomial exponential distribution(binomial-exponential 2 distribution,denoted as BE2).This model can well handle over-dispersed integer-valued time series data and the type of the distribution of the innovation sequence is simple.Furthermore,the new model has two adjustable parameters,which makes it very flexible and applicable when processing data.The main content of this thesis is as follows: Give some preliminary knowledge,including BE2 distribution,mixed Poisson-BE2 distribution and binomial thinning operator.To illustrate the properties of the above distributions,we give the data generating methods of these distributions and the sample path of different parameters.And also give the definition and statistical properties of the INAR model with PBE2 innovation sequence,including the mean,variance,covariance of the model and the stationarity and ergodicity of the model.Second,we use the conditional least squares(CLS)estimation and conditional maximum likelihood estimation(CML),and the large sample properties.Then,we conduct simulation study to illustrate the finite sample properties of the above estimators,and apply the new model to crime data and COVID-19 data,which shows that the new model can be better used to analyze over-dispersed data that widely existing in practice.