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Efficient Estimation of Autoregression Parameters and Innovation Distributions forSemiparametric Integer-Valued AR(p) Models (Revision of DP 2007-23)


  • 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)


Integer-valued autoregressive (INAR) processes have been introduced to model nonnegative integer-valued phenomena that evolve over time. The distribution of an INAR(p) process is essentially described by two parameters: a vector of autoregression coefficients and a probability distribution on the nonnegative integers, called an immigration or innovation distribution. Traditionally, parametric models are considered where the innovation distribution is assumed to belong to a parametric family. This paper instead considers a more realistic semiparametric INAR(p) model where there are essentially no restrictions on the innovation distribution. We provide an (semiparametrically) efficient estimator of both the autoregression parameters and the innovation distribution.

Suggested Citation

  • 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.
  • Handle: RePEc:tiu:tiucen:cef533d0-6b49-4ce9-8cd2-7a20a43d2dfb

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    Cited by:

    1. 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.
    2. Jentsch, Carsten & Leucht, Anne, 2014. "Bootstrapping Sample Quantiles of Discrete Data," Working Papers 14-15, University of Mannheim, Department of Economics.
    3. Jentsch, Carsten & Weiß, Christian, 2017. "Bootstrapping INAR models," Working Papers 17-02, University of Mannheim, Department of Economics.
    4. Germán Aneiros, 2012. "Comments on: Some recent theory for autoregressive count time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 439-441, September.


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