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Local asymptotic normality and efficient estimation for INAR(p) models

Author

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  • Feike C. Drost
  • Ramon Van Den Akker
  • Bas J. M. Werker

Abstract

. Integer‐valued autoregressive (INAR) processes have been introduced to model non‐negative integer‐valued phenomena that evolve in time. The distribution of an INAR(p) process is determined by two parameters: a vector of survival probabilities and a probability distribution on the non‐negative integers, called an immigration distribution. This paper provides an efficient estimator of the parameters, and in particular, shows that the INAR(p) model has the Local Asymptotic Normality property.

Suggested Citation

  • Feike C. Drost & Ramon Van Den Akker & Bas J. M. Werker, 2008. "Local asymptotic normality and efficient estimation for INAR(p) models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 783-801, September.
    • Handle: RePEc:bla:jtsera:v:29:y:2008:i:5:p:783-801
    DOI: 10.1111/j.1467-9892.2008.00581.x
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    1. Maria Eduarda Silva & Vera Lúcia Oliveira, 2005. "Difference Equations for the Higher Order Moments and Cumulants of the INAR(p) Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 17-36, January.
    2. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2006. "An Asymptotic Analysis of Nearly Unstable inar (1) Models," Other publications TiSEM 6e89d2b0-1d07-4f01-9b2f-5, Tilburg University, School of Economics and Management.
    3. Drost, Feike C. & van den Akker, Ramon & Werker, Bas J.M., 2008. "Note on integer-valued bilinear time series models," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 992-996, June.
    4. Kurt Brannas & Jorgen Hellstrom, 2001. "Generalized Integer-Valued Autoregression," Econometric Reviews, Taylor & Francis Journals, vol. 20(4), pages 425-443.
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    8. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2006. "An Asymptotic Analysis of Nearly Unstable inar (1) Models," Discussion Paper 2006-44, Tilburg University, Center for Economic Research.
    9. M. A. Al‐Osh & A. A. Alzaid, 1987. "First‐Order Integer‐Valued Autoregressive (Inar(1)) Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 261-275, May.
    10. Gourieroux, C. & Jasiak, J., 2004. "Heterogeneous INAR(1) model with application to car insurance," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 177-192, April.
    11. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(2), pages 241-257, June.
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    13. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2008. "Efficient Estimation of Autoregression Parameters and Innovation Distributions forSemiparametric Integer-Valued AR(p) Models (Revision of DP 2007-23)," Discussion Paper 2008-53, Tilburg University, Center for Economic Research.
    14. Ulf Böckenholt, 2003. "Analysing state dependences in emotional experiences by dynamic count data models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(2), pages 213-226, May.
    15. Paul D. Feigin & Richard L. Tweedie, 1985. "Random Coefficient Autoregressive Processes:A Markov Chain Analysis Of Stationarity And Finiteness Of Moments," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(1), pages 1-14, January.
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    Cited by:

    1. Mohamed Sadoun & Mohamed Bentarzi, 2021. "Locally asymptotically efficient estimation for parametric PINAR(p) models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 257-289, August.
    2. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2006. "An Asymptotic Analysis of Nearly Unstable inar (1) Models," Other publications TiSEM 6e89d2b0-1d07-4f01-9b2f-5, Tilburg University, School of Economics and Management.
    3. Mátyás Barczy & Márton Ispány & Gyula Pap, 2014. "Asymptotic Behavior of Conditional Least Squares Estimators for Unstable Integer-valued Autoregressive Models of Order 2," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 866-892, December.
    4. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2006. "An Asymptotic Analysis of Nearly Unstable inar (1) Models," Discussion Paper 2006-44, Tilburg University, Center for Economic Research.
    5. Ruijun Bu & Brendan McCabe & Kaddour Hadri, 2008. "Maximum likelihood estimation of higher‐order integer‐valued autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 973-994, November.
    6. 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.
    7. repec:tiu:tiutis:6b90fe6f-4de9-4192-9f4d-99ae9220af75 is not listed on IDEAS
    8. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2009. "The asymptotic structure of nearly unstable non negative integer-valued AR(1) models," Other publications TiSEM ac0494ae-7a32-43ca-b5b4-d, Tilburg University, School of Economics and Management.

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    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
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other

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