Robust estimation for general integer-valued autoregressive models based on the exponential-polynomial divergence

Abstract

In this study, we develop a robust estimator for integer-valued one-parameter exponential family autoregressive models, named general integer-valued autoregressive models. This model accommodates a broad class of integer-valued time series models. In particular, we propose a robust estimation method that minimizes the exponential-polynomial divergence (EPD) belonging to the Brègman divergence family. EPD subsumes the density power divergence (DPD), which has been extensively studied by many authors for the past decades. Under regularity conditions, the minimum EPD estimator (MEPDE) is shown to be consistent and asymptotically normal. Comparing the performance of MEPDE with the minimum DPD estimator, we substantiate the validity of MEPDE through a simulation study and real data analysis.

Keywords:

• Integer-valued time series model
• robust estimation
• minimum exponential-polynomial divergence estimator
• Brègman divergence
• one-parameter exponential family

Acknowledgments

We thank an AE and two anonymous reviewers for their careful reading and valuable comments to improve the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the 2022 Yeungnam University Research Grant (No. 222A061008) (B.Kim) and the Basic Science Research Program through the National Research Foundation of Korea (NRF) (No. 2021R1A2C1004009) (S. Lee).