IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v82y2012i5p942-948.html
   My bibliography  Save this article

On weak dependence conditions for Poisson autoregressions

Author

Listed:
  • Doukhan, Paul
  • Fokianos, Konstantinos
  • Tjøstheim, Dag

Abstract

We consider generalized linear models for regression modeling of count time series. We give easily verifiable conditions for obtaining weak dependence for such models. These results enable the development of maximum likelihood inference under minimal conditions. Some examples which are useful to applications are discussed in detail.

Suggested Citation

  • Doukhan, Paul & Fokianos, Konstantinos & Tjøstheim, Dag, 2012. "On weak dependence conditions for Poisson autoregressions," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 942-948.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:942-948
    DOI: 10.1016/j.spl.2012.01.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212000259
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Doukhan, Paul & Wintenberger, Olivier, 2008. "Weakly dependent chains with infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1997-2013, November.
    3. 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.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Fokianos, Konstantinos & Tjøstheim, Dag, 2011. "Log-linear Poisson autoregression," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 563-578, March.
    6. Richard A. Davis, 2003. "Observation-driven models for Poisson counts," Biometrika, Biometrika Trust, vol. 90(4), pages 777-790, December.
    7. Konstantinos Fokianos & Dag Tjøstheim, 2012. "Nonlinear Poisson autoregression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1205-1225, December.
    8. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kang, Jiwon & Song, Junmo, 2015. "Robust parameter change test for Poisson autoregressive models," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 14-21.
    2. Aknouche, Abdelhakim & Bendjeddou, Sara, 2016. "Negative binomial quasi-likelihood inference for general integer-valued time series models," MPRA Paper 76574, University Library of Munich, Germany, revised 03 Feb 2017.
    3. Kheifets, Igor & Velasco, Carlos, 2017. "New goodness-of-fit diagnostics for conditional discrete response models," Journal of Econometrics, Elsevier, vol. 200(1), pages 135-149.
    4. 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.
    5. repec:eee:stapro:v:134:y:2018:i:c:p:15-21 is not listed on IDEAS
    6. Jentsch, Carsten & Leucht, Anne, 2014. "Bootstrapping Sample Quantiles of Discrete Data," Working Papers 14-15, University of Mannheim, Department of Economics.
    7. Cui, Yunwei & Zheng, Qi, 2017. "Conditional maximum likelihood estimation for a class of observation-driven time series models for count data," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 193-201.
    8. Hanan Elsaied & Roland Fried, 2014. "Robust Fitting Of Inarch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 517-535, November.
    9. Moysiadis, Theodoros & Fokianos, Konstantinos, 2014. "On binary and categorical time series models with feedback," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 209-228.
    10. Chen, Cathy W.S. & Lee, Sangyeol, 2016. "Generalized Poisson autoregressive models for time series of counts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 51-67.
    11. Jiwon Kang & Sangyeol Lee, 2014. "Parameter Change Test for Poisson Autoregressive Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1136-1152, December.
    12. Fokianos, Konstantinos & Moysiadis, Theodoros, 2017. "Binary time series models driven by a latent process," Econometrics and Statistics, Elsevier, vol. 2(C), pages 117-130.
    13. Kang, Jiwon & Lee, Sangyeol, 2014. "Minimum density power divergence estimator for Poisson autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 44-56.
    14. Aknouche, Abdelhakim & Bentarzi, Wissam & Demouche, Nacer, 2017. "On periodic ergodicity of a general periodic mixed Poisson autoregression," MPRA Paper 79650, University Library of Munich, Germany.
    15. Doukhan, Paul & Fokianos, Konstantinos & Tjøstheim, Dag, 2013. "Correction to “On weak dependence conditions for Poisson autoregressions” [Statist. Probab. Lett. 82 (2012) 942–948]," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1926-1927.
    16. Doukhan, Paul & Fokianos, Konstantinos & Li, Xiaoyin, 2012. "On weak dependence conditions: The case of discrete valued processes," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1941-1948.
    17. repec:bla:jtsera:v:38:y:2017:i:6:p:880-894 is not listed on IDEAS
    18. 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.
    19. Cui, Yunwei & Wu, Rongning, 2016. "On conditional maximum likelihood estimation for INGARCH(p,q) models," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 1-7.
    20. Carsten Jentsch & Anne Leucht, 2016. "Bootstrapping sample quantiles of discrete data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(3), pages 491-539, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:942-948. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.