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On robust estimation of negative binomial INARCH models

Author

Listed:
  • Hanan Elsaied

    (Suez Canal University)

  • Roland Fried

    (TU Dortmund University)

Abstract

We discuss robust estimation of INARCH models for count time series, where each observation conditionally on its past follows a negative binomial distribution with a constant scale parameter, and the conditional mean depends linearly on previous observations. We develop several robust estimators, some of them being computationally fast modifications of methods of moments, and some rather efficient modifications of conditional maximum likelihood. These estimators are compared to related recent proposals using simulations. The usefulness of the proposed methods is illustrated by a real data example.

Suggested Citation

  • Hanan Elsaied & Roland Fried, 2021. "On robust estimation of negative binomial INARCH models," METRON, Springer;Sapienza Università di Roma, vol. 79(2), pages 137-158, August.
    • Handle: RePEc:spr:metron:v:79:y:2021:i:2:d:10.1007_s40300-021-00207-8
    DOI: 10.1007/s40300-021-00207-8
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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. 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.
    5. William H. Aeberhard & Eva Cantoni & Stephane Heritier, 2014. "Robust inference in the negative binomial regression model with an application to falls data," Biometrics, The International Biometric Society, vol. 70(4), pages 920-931, December.
    6. Fukang Zhu, 2011. "A negative binomial integer‐valued GARCH model," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(1), pages 54-67, January.
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    8. Jensen, Søren Tolver & Rahbek, Anders, 2007. "On The Law Of Large Numbers For (Geometrically) Ergodic Markov Chains," Econometric Theory, Cambridge University Press, vol. 23(4), pages 761-766, August.
    9. N. E. Breslow, 1984. "Extra‐Poisson Variation in Log‐Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(1), pages 38-44, March.
    10. Vasiliki Christou & Konstantinos Fokianos, 2014. "Quasi-Likelihood Inference For Negative Binomial Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 55-78, January.
    11. Bernard Garel & Marc Hallin, 1999. "Rank-Based Autoregressive Order Identification," ULB Institutional Repository 2013/127976, ULB -- Universite Libre de Bruxelles.
    12. Ieva Axt & Roland Fried, 2020. "On variance estimation under shifts in the mean," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 417-457, September.
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    Cited by:

    1. Fokianos, Konstantinos & Fried, Roland & Kharin, Yuriy & Voloshko, Valeriy, 2022. "Statistical analysis of multivariate discrete-valued time series," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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