Random Environment Based On The Generalized Signed Thinning Operator INAR Random Coefficient Model

In real life,integer-valued time series data can be seen everywhere,such as the number of daily business of a bank,the number of registered people in a window of a hospital,etc.With the increasing influence of the integer-valued time series model,statisticians begin to pay attention to the change of the integer-valued time series model itself and its disturbance term under the influence of the environment.To solve the problem of the change of the integer-valued time series model caused by the sudden change of environment,this paper introduces the random environment process into the random coefficient INAR(1)model based on the generalized signed thinning operator,establishes the random coefficient INAR(1)model based on the generalized signed thinning operator in the random environment,and extends the new model to the p-order,and establishes the random coefficient high order INAR model based on the generalized signed thinning operator in the random environment.The content structure of the article is as follows: the first chapter is the introduction,which briefly describes the background significance and present situation of the previous work on the integer-valued autoregressive model.The second chapter proposes a random coefficient INAR(1)model based on generalized signed thinning operator in random environment,gives the definition of the new model,discusses the conditional expectation,conditional variance,covariance function and other properties of the model.The Yule-Walker method is used to estimate the model parameters.Chapter 3 extends the random coefficient INAR(1)model based on generalized signed thinning operator in the random environment proposed in chapter 2 to the case of higher order,studies the conditional expectation,conditional variance,and covariance function of the new higher order model,and proves that the Yule-Walker estimators are strongly consistent.Finally,the good performance of the estimators under finite samples are verified by numerical simulation experiments.The fourth chapter is the summary and prospect.