Generalized RCINAR(p) Process with Signed Thinning Operator

Abstract

We propose a new integer-valued time series process, called generalized pth-order random coefficient integer-valued autoregressive process with signed thinning operator. This kind of process is appropriate for modeling negative integer-valued time series; strict stationarity and ergodicity of the process are established. Estimators of the model's parameters are derived and their properties are studied via simulation. We apply our process to a real data example.

Keywords:

• Bootstrap
• Generalized signed thinning
• Integer-valued time series
• Random coefficient
• Strict stationarity and ergodicity

Mathematics Subject Classification:

• 62M10
• 62F10

Acknowledgments

We thank the referee for valuable suggestions and comments which greatly improved the article. This work is supported by National Natural Science Foundation of China (No. 10971081, J0730101), Specialized Research Fund for the Doctoral Program of Higher Education (No. 20070183023), Program for New Century Excellent Talents in University (NCET-08-237), Scientific Research Fund of Jilin University (No. 200810024), 985 project of Jilin University and Graduate Innovation Fund of Jilin University (No. 20101042).

Notes

^‡300 realizations have been used for all sample sizes.

^‡300 realizations have been used for all sample sizes.