Statistical Inference For INAR(1) Model With Covariate-driven Mixture Probability

In the era of big data,choosing the appropriate time series model to analyze the real data can help us to better solve the practical problems in life.For continuous data,the classical autoregressive model,the moving average model and the autoregressive moving average model are good for modeling.However,for data with integer values,that is,counting data,the modeling effect of the above model is not good,which indicates that the above time series model cannot explain the generation mechanism of counting data hiding,thus produced a big deviation.Many of the data we encounter in our daily life are count data.In order to better analyze and predict this kind of data,scholars begin to study the statistical inference and application of time series of integer values.The first-order integer value autoregression(INAR(1))process based on the binomial thinning operator is favored by scholars.On the basis of this model,many integer value time series models with research value are derived.Among them,the random coefficient integer value autoregressive model considers the randomness of thinning parameters,assumes the thinning parameters as a column of independent and equally distributed random variables,and expands INAR(1)process.However,with the futher study of research,scholars found that the randomness of thinning parameters may be affected by some observable explanatory variables,such as the observed value or covariates,so therefore proposed the random coefficient INAR(1)process driven by the observed value or covariates.Considering the influence of covariates on the mixture probability,we propose an INAR(1)model based on the Logistic structure,and calculate the conditional moment of the model,using the conditional maximum likelihood and Bayesian estimation methods to estimate the model parameters.With the help of Matlab software,the numerical simulation with covariates of one and two dimensions respectively can verify the effectiveness of the estimation method,and some numerical results of the estimator are obtained.Finally,a set of actual data is selected for example analysis,and the fitting effect is compared with the classic INAR(1)model.The results show that the model proposed in this paper is more suitable to fit this set of data,which confirms that the model is helpful in solving practical problems.