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On higher-order moments of INGARCH processes

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  • Weiß, Christian H.

Abstract

For important count distributions, such as (zero-inflated) Poisson and (negative-)binomial, the kth factorial moment is proportional to the kth power of the mean. This property is utilized to derive a general approach for computing higher-order moments of integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) processes. The proposed approach covers a wide range of existing model specifications, and its potential benefits are illustrated by an analysis of skewness and excess kurtosis in INGARCH processes.

Suggested Citation

  • Weiß, Christian H., 2024. "On higher-order moments of INGARCH processes," Statistics & Probability Letters, Elsevier, vol. 214(C).
    • Handle: RePEc:eee:stapro:v:214:y:2024:i:c:s0167715224001676
    DOI: 10.1016/j.spl.2024.110198
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    References listed on IDEAS

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    1. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
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    4. Heinen, Andreas, 2003. "Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model," MPRA Paper 8113, University Library of Munich, Germany.
    5. HEINEN, Andreas & RENGIFO, Erick, 2003. "Multivariate modelling of time series count data: an autoregressive conditional Poisson model," LIDAM Discussion Papers CORE 2003025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Weiß, Christian H., 2010. "INARCH(1) processes: Higher-order moments and jumps," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1771-1780, December.
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