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INARCH(1) processes: Higher-order moments and jumps

  • Weiß, Christian H.
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    The INARCH(1) model is a simple but practically relevant, two-parameter model for processes of overdispersed counts with an autoregressive serial dependence structure. We derive closed-form expressions for the joint (central) moments and cumulants of the INARCH(1) model up to order 4. These expressions are applied to derive the moments of jumps in INARCH(1) processes. We illustrate this kind of application with a real-data example, and outline further potential applications.

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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 80 (2010)
    Issue (Month): 23-24 (December)
    Pages: 1771-1780

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    Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1771-1780
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    1. Weiß, Christian H., 2009. "Jumps in binomial AR(1) processes," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2012-2019, October.
    2. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
    3. HEINEN, Andreas & RENGIFO, Erick, 2003. "Multivariate modelling of time series count data: an autoregressive conditional Poisson model," CORE Discussion Papers 2003025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Fukang Zhu & Dehui Wang, 2011. "Estimation and testing for a Poisson autoregressive model," Metrika, Springer, vol. 73(2), pages 211-230, March.
    5. HEINEN, Andréas, 2003. "Modelling time series count data: an autoregressive conditional Poisson model," CORE Discussion Papers 2003062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Christian Weiß, 2009. "Modelling time series of counts with overdispersion," Statistical Methods and Applications, Springer, vol. 18(4), pages 507-519, November.
    7. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer, vol. 92(3), pages 319-341, August.
    8. René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer-Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
    9. Jung, Robert C. & Kukuk, Martin & Liesenfeld, Roman, 2006. "Time series of count data: modeling, estimation and diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2350-2364, December.
    10. Zhu, Fukang & Wang, Dehui, 2010. "Diagnostic checking integer-valued ARCH(p) models using conditional residual autocorrelations," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 496-508, February.
    11. Konstantinos Fokianos & Roland Fried, 2010. "Interventions in INGARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(3), pages 210-225, 05.
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