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Treating missing values in INAR(1) models

Author

Listed:
  • Andersson, Jonas

    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

  • Karlis, Dimitris

    (Department of Statistics, Athens University of Economics and Business)

Abstract

Time series models for count data have found increased interest in recent days. The existing literature refers to the case of data that have been fully observed. In the present paper, methods for estimating the parameters of the first-order integer-valued autoregressive model in the presence of missing data are proposed. The first method maximizes a conditional likelihood constructed via the observed data based on the k-step-ahead conditional distributions to account for the gaps in the data. The second approach is based on an iterative scheme where missing values are imputed in order to update the estimated parameters. The first method is useful when the predictive distributions have simple forms. We derive in full details this approach when the innovations are assumed to follow a finite mixture of Poisson distributions. The second method is applicable when there are not closed form expressions for the conditional likelihood or they are hard to derive. Simulation results and comparisons of the methods are reported. The proposed methods are applied to a data set concerning syndromic surveillance during the Athens 2004 Olympic Games.

Suggested Citation

  • Andersson, Jonas & Karlis, Dimitris, 2008. "Treating missing values in INAR(1) models," Discussion Papers 2008/14, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2008_014
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    File URL: http://hdl.handle.net/11250/164126
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    References listed on IDEAS

    as
    1. Kurt Brannas & Jorgen Hellstrom, 2001. "Generalized Integer-Valued Autoregression," Econometric Reviews, Taylor & Francis Journals, vol. 20(4), pages 425-443.
    2. Freeland, R. K. & McCabe, B. P. M., 2004. "Forecasting discrete valued low count time series," International Journal of Forecasting, Elsevier, vol. 20(3), pages 427-434.
    3. 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.
    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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Imputation; Markov Chain EM algorithm; mixed Poisson; discrete valued time series;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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