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Local Asymptotic Normality and Efficient Estimation for inar (P) Models

Author

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  • Drost, F.C.

    (Tilburg University, Center For Economic Research)

  • van den Akker, R.

    (Tilburg University, Center For Economic Research)

  • Werker, B.J.M.

    (Tilburg University, Center For Economic Research)

Abstract

Integer-valued autoregressive (INAR) processes have been introduced to model nonnegative integervalued 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 nonnegative integers, called an immigration or innovation 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

  • Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2006. "Local Asymptotic Normality and Efficient Estimation for inar (P) Models," Discussion Paper 2006-45, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:95ec06ea-005b-4c08-a2e6-f5901d66e640
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    References listed on IDEAS

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    1. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
    2. Maria Eduarda Silva & Vera Lucia 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.
    3. R. K. Freeland & B. P. M. McCabe, 2004. "Analysis of low count time series data by poisson autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 701-722, September.
    4. 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.
    5. 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.
    6. Elisabet Berglund & Kurt Brännäs, 2001. "Plants' entry and exit in Swedish municipalities," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 35(3), pages 431-448.
    7. Nikas Rudholm, 2001. "Entry and the Number of Firms in the Swedish Pharmaceuticals Market," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 19(3), pages 351-364, November.
    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. 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.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    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.

    More about this item

    Keywords

    count data; integer-valued time series; information loss structure;

    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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