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, Volume 27, Issue 1, pp 52–69 | Cite as

Asymptotic normality and parameter change test for bivariate Poisson INGARCH models

  • Youngmi Lee
  • Sangyeol Lee
  • Dag Tjøstheim
Original Paper

Abstract

In this paper, we consider the problem of testing for a parameter change in bivariate Poisson integer-valued GARCH(1, 1) models, constructed via a trivariate reduction method of independent Poisson variables. We verify that the conditional maximum-likelihood estimator of the model parameters is asymptotically normal. Then, based on these results, we construct CMLE- and residual-based CUSUM tests and derive that their limiting null distributions are a function of independent Brownian bridges. A simulation study and real data analysis are conducted for illustration.

Keywords

Time series of counts Bivariate Poisson INGARCH model Test for a parameter change CUSUM test 

Mathematics Subject Classification

62M10 62G20 

Notes

Acknowledgements

We thank the Editor and the two anonymous referees for their careful reading and valuable comments to improve the quality of the paper. Sangyeol Lee’s 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. 2015R1A2A2A010003894).

Supplementary material

11749_2016_510_MOESM1_ESM.pdf (71 kb)
Supplementary material 1 (pdf 71 KB)

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2016

Authors and Affiliations

  1. 1.Department of StatisticsSeoul National UniversitySeoulKorea
  2. 2.Department of MathematicsUniversity of BergenBergenNorway

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