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Time‐Varying Dispersion Integer‐Valued GARCH Models

Author

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  • Wagner Barreto‐Souza
  • Luiza S. C. Piancastelli
  • Konstantinos Fokianos
  • Hernando Ombao

Abstract

We introduce a general class of INteger‐valued Generalized AutoRegressive Conditionally Heteroscedastic (INGARCH) processes by allowing simultaneously time‐varying mean and dispersion parameters. We call such models time‐varying dispersion INGARCH (tv‐DINGARCH) models. More specifically, we consider mixed Poisson INGARCH models and allow for dynamic modeling of both mean and dispersion parameters. We derive conditions to obtain stochastic stability of tv‐DINGARCH processes. Additionally, we study maximum likelihood estimation in detail including its asymptotic distribution. A restricted bootstrap procedure is proposed for testing constant dispersion against time‐varying dispersion. Monte Carlo simulation studies are presented for checking point estimation, standard errors, and the performance of the restricted bootstrap approach. We apply the tv‐DINGARCH process to model the weekly number of reported measles infections in North Rhine‐Westphalia, Germany, from January 2001 to May 2013, and compare its performance to the ordinary INGARCH approach.

Suggested Citation

  • Wagner Barreto‐Souza & Luiza S. C. Piancastelli & Konstantinos Fokianos & Hernando Ombao, 2026. "Time‐Varying Dispersion Integer‐Valued GARCH Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 47(4), pages 839-853, July.
    • Handle: RePEc:bla:jtsera:v:47:y:2026:i:4:p:839-853
    DOI: 10.1111/jtsa.12838
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