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

1. LI Qi
College of Mathematics, Changchun Normal University, Changchun 130032, China.
CHEN Huaping
School of Mathematics and Statistics, Henan University, Kaifeng 475004, China.
ZHU Fukang (Corresponding author)
School of Mathematics, Jilin University, Changchun 130012, China. Email: zfk8010@163.com.
• Online:2021-08-25 Published:2021-08-10

LI Qi · CHEN Huaping · ZHU Fukang. Robust Estimation for Poisson Integer-Valued GARCH Models Using a New Hybrid Loss[J]. Journal of Systems Science and Complexity, 2021, 34(4): 1578-1596.

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.
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