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Mallows’ quasi-likelihood estimation for log-linear Poisson autoregressions

Author

Listed:
  • Stella Kitromilidou

    (University of Cyprus)

  • Konstantinos Fokianos

    (University of Cyprus)

Abstract

We consider the problems of robust estimation and testing for a log-linear model with feedback for the analysis of count time series. We study inference for contaminated data with transient shifts, level shifts and additive outliers. It turns out that the case of additive outliers deserves special attention. We propose a robust method for estimating the regression coefficients in the presence of interventions. The resulting robust estimators are asymptotically normally distributed under some regularity conditions. A robust score type test statistic is also examined. The methodology is applied to real and simulated data.

Suggested Citation

  • Stella Kitromilidou & Konstantinos Fokianos, 2016. "Mallows’ quasi-likelihood estimation for log-linear Poisson autoregressions," Statistical Inference for Stochastic Processes, Springer, vol. 19(3), pages 337-361, October.
    • Handle: RePEc:spr:sistpr:v:19:y:2016:i:3:d:10.1007_s11203-015-9131-z
    DOI: 10.1007/s11203-015-9131-z
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    References listed on IDEAS

    as
    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.
    2. Konstantinos Fokianos & Roland Fried, 2010. "Interventions in INGARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(3), pages 210-225, May.
    3. Lô, Serigne N. & Ronchetti, Elvezio, 2009. "Robust and accurate inference for generalized linear models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2126-2136, October.
    4. Andrew C. Harvey, 1990. "The Econometric Analysis of Time Series, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026208189x, December.
    5. Hanan Elsaied & Roland Fried, 2014. "Robust Fitting Of Inarch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 517-535, November.
    6. Douc, R. & Doukhan, P. & Moulines, E., 2013. "Ergodicity of observation-driven time series models and consistency of the maximum likelihood estimator," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2620-2647.
    7. Mátyás Barczy & Márton Ispány & Gyula Pap & Manuel Scotto & Maria Silva, 2012. "Additive outliers in INAR(1) models," Statistical Papers, Springer, vol. 53(4), pages 935-949, November.
    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. Fokianos, Konstantinos & Tjøstheim, Dag, 2011. "Log-linear Poisson autoregression," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 563-578, March.
    10. Cantoni E. & Ronchetti E., 2001. "Robust Inference for Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1022-1030, September.
    11. Nora Muler & Victor J. Yohai, 2002. "Robust estimates for arch processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(3), pages 341-375, May.
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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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