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Power periodic threshold GARCH model: Structure and estimation

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  • Hafida Guerbyenne
  • Abderrahim Kessira

Abstract

In this paper, we introduce and study the Power Periodic Threshold GARCH Model (PPTGARCH). We give the necessary and sufficient conditions for the existence of the unique strictly periodically stationary solution of the model and the necessary and sufficient conditions for the existence of moments. A sufficient condition for the periodic geometric ergodicity and β – mixing property using the uniform countable additivity condition is given. We prove the consistency and asymptotic normality of the Quasi-Maximum Likelihood estimator (QMLE) of the parameters. Simulation studies to illustrate consistency and asymptotic normality of the estimators for different underlying error distributions are presented.

Suggested Citation

  • Hafida Guerbyenne & Abderrahim Kessira, 2019. "Power periodic threshold GARCH model: Structure and estimation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(19), pages 4834-4860, October.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:19:p:4834-4860
    DOI: 10.1080/03610926.2018.1496258
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