Residual-based CUSUM of squares test for Poisson integer-valued GARCH models

ABSTRACT

This study considers the problem of testing for a parameter change in integer-valued time series models in which the conditional density of current observations is assumed to follow a Poisson distribution. As a test, we consider the CUSUM of the squares test based on the residuals from INGARCH models and find that the test converges weakly to the supremum of a Brownian bridge. A simulation study demonstrates its superiority to the residual and standardized residual-based CUSUM tests of Kang and Lee [Parameter change test for Poisson autoregressive models. Scand J Statist. 2014;41:1136–1152] and Lee and Lee [CUSUM tests for general nonlinear inter-valued GARCH models: comparison study. Ann Inst Stat Math. 2019;71:1033–1057.] as well as the CUSUM of squares test based on standardized residuals.

KEYWORDS:

• Time series of counts
• integer-valued GARCH models
• parameter change test
• residual-based CUSUM of squares test

Acknowledgements

I would like to thank an AE and one referee for their careful reading and valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Sangyeol Lee http://orcid.org/0000-0003-1109-6768

Additional information

Funding

This research is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (No. 2018R1A2A2A05019433).