A study of RCINAR(1) process with generalized negative binomial marginals

Abstract

To better describe the data whose variance is greater than mean in time series analysis, this paper introduces the RCINAR(1) process with generalized negative binomial marginals. The related estimations of this process are considered using Yule-Walker, modified conditional least squares, conditional maximum likelihood and Bayesian methods. The asymptotic properties of the estimators are established. Some simulations are conducted to verify the proposed estimation methods and a real example is proposed to illustrate the advantages of our model.

Keywords:

• Autoregressive process
• integer-valued time series
• parameter estimation
• random coefficient

Acknowledgments

This work is supported by National Natural Science Foundation of China (No. 11731015, 11571051, J1310022, 11501241), Natural Science Foundation of Jilin Province (No. 20150520053JH, 20170101057JC, 20180101216JC), Program for Changbaishan Scholars of Jilin Province (2015010), and Science and Technology Program of Jilin Educational Department during the “13th Five-Year” Plan Period (No. 2016-399).

Disclosure statement

No potential conflict of interest was reported by the authors.