Test of parameter changes in a class of observation-driven models for count time series

Abstract

This paper investigates the parameter-change tests for a class of observation-driven models for count time series. We propose two cumulative sum (CUSUM) test procedures for detection of changes in model parameters. Under regularity conditions, the asymptotic null distributions of the test statistics are established. In addition, the integer-valued generalized autoregressive conditional heteroskedastic (INGARCH) processes with conditional negative binomial distributions are investigated. The developed techniques are examined through simulation studies and also are illustrated using an empirical example.

Keywords:

• Diagnostic tests
• change-point detection
• negative binomial INGARCH model
• nonlinear models
• time series of counts

Acknowledgments

The authors would like to thank an anonymous referee for the valuable comments. The research of Rongning Wu was supported in part by a PSC-CUNY award, jointly funded by The Professional Staff Congress and The City University of New York.