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Efficient Estimation of Autoregression Parameters and Innovation Distributions for Semiparametric Integer-Valued AR(p) Models (Subsequently replaced by DP 2008-53)

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Author Info

  • Drost, F.C.
  • Akker, R. van den
  • Werker, B.J.M.

    (Tilburg University, Center for Economic Research)

Abstract

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: essentially there are no restrictions on the innovation distribution. We provide an (semiparametrically) efficient estimator of the autoregression parameters and the innovation distribution.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2007-23.

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Date of creation: 2007
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Handle: RePEc:dgr:kubcen:200723

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Web page: http://center.uvt.nl

Related research

Keywords: count data; nonparametric maximum likelihood; infinite-dimensional Z-estimator; semiparametric efficiency;

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References

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  1. Drost, F.C. & Akker, R. van den & 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.
  2. Drost, F.C. & Klaasens, C.A.J. & Werker, B.J.M., 1994. "Adaptive Estimation in Time Series Models," Papers 9488, Tilburg - Center for Economic Research.
  3. 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.
  4. Robert Jung & Gerd Ronning & A. Tremayne, 2005. "Estimation in conditional first order autoregression with discrete support," Statistical Papers, Springer, vol. 46(2), pages 195-224, April.
  5. McCabe, B.P.M. & Martin, G.M., 2005. "Bayesian predictions of low count time series," International Journal of Forecasting, Elsevier, vol. 21(2), pages 315-330.
  6. Brännäs, Kurt & Quoreshi, Shahiduzzaman, 2004. "Integer-Valued Moving Average Modelling of the Number of Transactions in Stocks," UmeÃ¥ Economic Studies 637, Umeå University, Department of Economics.
  7. Peter Neal & T. Subba Rao, 2007. "MCMC for Integer-Valued ARMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(1), pages 92-110, 01.
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