Abstract
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 data-driven 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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This paper was 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.
This paper was recommended for publication by Editor LI Qizhai.
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Li, Q., Chen, H. & Zhu, F. Robust Estimation for Poisson Integer-Valued GARCH Models Using a New Hybrid Loss. J Syst Sci Complex 34, 1578–1596 (2021). https://doi.org/10.1007/s11424-020-9344-0
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DOI: https://doi.org/10.1007/s11424-020-9344-0