Robust Estimation for Poisson Integer-Valued GARCH Models Using a New Hybrid Loss  

作　　者：LI Qi CHEN Huaping ZHU Fukang 

机构地区：[1]College of Mathematics,Changchun Normal University,Changchun 130032,China [2]School of Mathematics and Statistics,Henan University,Kaifeng 475004,China [3]School of Mathematics,Jilin University,Changchun 130012,China

出　　处：《Journal of Systems Science & Complexity》2021年第4期1578-1596,共19页系统科学与复杂性学报（英文版）

基　　金：supported by Research Start-up Fund of Changchun Normal University;Natural Science Found of Changchun Normal University under Grant No.2018-004;the National Natural Science Foundation of China under Grant Nos.11871027 and 11731015;Cultivation Plan for Excellent Young Scholar Candidates of Jilin University。

摘　　要：The Poisson integer-valued GARCH model is a popular tool in modeling time series of counts.The commonly used maximum likelihood estimator is strongly influenced by outliers,so there is a need to develop a robust M-estimator for this model.This paper has three aims.First,the authors propose a new loss function,which is a hybrid of the tri-weight loss for relatively small errors and the exponential squared loss for relatively large ones.Second,Mallows’quasi-likelihood estimator(MQLE)is proposed as an M-estimator and its existence,uniqueness,consistency and asymptotic normality are established.In addition,a data-adaptive algorithm for computing MQLE is given based on a datadriven selection of tuning parameters in the loss function.Third,simulation studies and analysis of a real example are conducted to illustrate the performance of the new estimator,and a comparison with existing estimators is made.

关 键 词：Loss function M-ESTIMATION time series of counts tuning parameter 

分 类 号：O212.1[理学—概率论与数理统计]