MB-bootstrap Forecasting Method For INAR(1) Model Based On Negative Binomial Thinning Operator

In reality,integer-valued time series data are very common,such as the number of flights taking off and landing each month,the number of people entering and leaving the library every day,the change in the number of a certain biological population,and the number of qualified products produced by a certain assembly line per hour,etc..These data widely exist in various social fields such as insurance,industry,medical and health care.Compared with traditional time series models,integer-valued time series models can describe the generation mechanism of integer-valued data well,so they have unique advantages in analysis and forecast.In terms of estimation and forecast of time series models,the bootstrap method is a commonly used non-parametric method,but related research is mainly based on traditional time series models,and there is relatively little discussion on bootstrap method of integer-valued time series.Recently,Bisaglia and Gerolimetto(2019)proposed a model-based bootstrap method(abbreviated as MB-bootstrap),and applied it to the INAR(1)model based on the binomial thinning operator to illustrate the advantages of this mothed.This thesis aims to promote the application scope of the MB-bootstrap method,and explore how to use this method to estimate parameters and make forecast for the INAR(1)model based on the negative binomial thinning operator.We first review the research and development process of the INAR model,and then the definition,basic properties and some parameter estimation methods of the INAR(1)model based on the negative binomial thinning operator are introduced,as well as the implementation process of several different bootstrap methods,including the Block Bootstrap method,the bootstrap method(abbreviated as CKP method)proposed by Cardinal et al.(1999)and Kim and Park(2008)and the MB-bootstrap method considered in this thesis.Secondly,the MB-bootstrap method,Block Bootstrap method,CKP method and Monte Carlo method are compared based on estimated bias and estimated mean square error,and the effectiveness of the MB-bootstrap method on estimating the parameter? in the INAR(1)model based on the negative binomial thinning operator is investigated.Then,by comparing the forecast mean square error,forecast mean absolute error and forecast mean coverage,we illustrate the good performance of the MB-bootstrap method in forecasting.Lastly,we conduct a real data analysis and the obtained results show that the statistical inference for the INAR(1)model based on the negative binomial thinning operator using the MB-bootstrap method has certain competitiveness in practice.