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Poisson QMLE of Count Time Series Models

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  • Ali Ahmad
  • Christian Francq

Abstract

Regularity conditions are given for the consistency of the Poisson quasi-maximum likelihood estimator of the conditional mean parameter of a count time series model. The asymptotic distribution of the estimator is studied when the parameter belongs to the interior of the parameter space and when it lies at the boundary. Tests for the significance of the parameters and for constant conditional mean are deduced. Applications to specific integer-valued autoregressive (INAR) and integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models are considered. Numerical illustrations, Monte Carlo simulations and real data series are provided.
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Suggested Citation

  • Ali Ahmad & Christian Francq, 2016. "Poisson QMLE of Count Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 291-314, May.
  • Handle: RePEc:bla:jtsera:v:37:y:2016:i:3:p:291-314
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    File URL: http://hdl.handle.net/10.1111/jtsa.12167
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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.
    2. M. Kachour & L. Truquet, 2011. "A p‐Order signed integer‐valued autoregressive (SINAR(p)) model," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(3), pages 223-236, May.
    3. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
    4. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    5. repec:dau:papers:123456789/10571 is not listed on IDEAS
    6. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    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. Francq, Christian & Wintenberger, Olivier & Zakoïan, Jean-Michel, 2013. "GARCH models without positivity constraints: Exponential or log GARCH?," Journal of Econometrics, Elsevier, vol. 177(1), pages 34-46.
    9. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    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. 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.
    12. 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).
    13. Fokianos, Konstantinos & Tjøstheim, Dag, 2011. "Log-linear Poisson autoregression," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 563-578, March.
    14. Fukang Zhu, 2011. "A negative binomial integer‐valued GARCH model," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(1), pages 54-67, January.
    15. 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).
    16. Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
    17. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    18. Feike C. Drost & Ramon van den Akker & Bas J. M. Werker, 2009. "Efficient estimation of auto‐regression parameters and innovation distributions for semiparametric integer‐valued AR(p) models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 467-485, April.
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    Citations

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    Cited by:

    1. 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.
    2. Rasmus Søndergaard Pedersen & Anders Rahbek, 2017. "Testing Garch-X Type Models," Discussion Papers 17-15, University of Copenhagen. Department of Economics.
    3. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos & Touche, Nassim, 2019. "Integer-valued stochastic volatility," MPRA Paper 91962, University Library of Munich, Germany, revised 04 Feb 2019.
    4. repec:eee:stapro:v:134:y:2018:i:c:p:15-21 is not listed on IDEAS
    5. 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.
    6. Aknouche, Abdelhakim & Francq, Christian, 2018. "Count and duration time series with equal conditional stochastic and mean orders," MPRA Paper 90838, University Library of Munich, Germany.
    7. repec:spr:testjl:v:27:y:2018:i:2:d:10.1007_s11749-017-0552-4 is not listed on IDEAS
    8. 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.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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