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Treating missing values in INAR(1) models

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  • 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.

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Bibliographic Info

Paper provided by Department of Business and Management Science, Norwegian School of Economics in its series Discussion Papers with number 2008/14.

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Length: 17 pages
Date of creation: 13 Aug 2008
Date of revision:
Handle: RePEc:hhs:nhhfms:2008_014

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Web page: http://www.nhh.no/en/research-faculty/department-of-business-and-management-science.aspx
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Keywords: Imputation; Markov Chain EM algorithm; mixed Poisson; discrete valued time series;

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  1. 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.
  2. 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.
  3. Brännäs, Kurt & Hellström, Jörgen, 1999. "Generalized Integer-Valued Autoregression," UmeÃ¥ Economic Studies 501, Umeå University, Department of Economics.
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