Bootstrap Method For Confidence Interval In NGINAR(1)model

First-order integer-valued autoregressive(INAR(1))process has been widely applied to modelling and the counting data.Series of this kind model are encountered in many fileds,e.g.,in insurance theory,medicine,economy.In this paper,we introduce a new stationary integer-valued autoregressive process of first order with geometric marginal based on the negative binomial thinning operator which contains geometric counting series.We will focus on how to use bootstrap procedure to predict and estimate the confidence interval of some statistics under this model.We introduce some structural properties such as the mean,variance,marginal distribution,etc,and give three estimation methods of parameters.We explain the defects of applying bootstrap method of traditional AR model to integer-valued time series,and propose a general bootstrap implementation.And we present some mild conditions for bootstrap method.We investigate the performance of the discussed bootstrap procedure under the NGINAR(1)model in an extensive simulation study,where we analyze the true coverage of 95% confidence intervals for diverse statistics.Finally we apply parametric bootstrap method to the real data examples,and get a good result.