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Treating missing values in INAR(1) models: An application to syndromic surveillance data

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  • Jonas Andersson
  • Dimitris Karlis

Abstract

Time‐series models for count data have found increased interest in recent years. The existing literature refers to the case of data that have been fully observed. In this article, 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 so as 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 no closed form expression for the conditional likelihood or they are hard to derive. The proposed methods are applied to a dataset concerning syndromic surveillance during the Athens 2004 Olympic Games.

Suggested Citation

  • Jonas Andersson & Dimitris Karlis, 2010. "Treating missing values in INAR(1) models: An application to syndromic surveillance data," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 12-19, January.
    • Handle: RePEc:bla:jtsera:v:31:y:2010:i:1:p:12-19
    DOI: 10.1111/j.1467-9892.2009.00636.x
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    References listed on IDEAS

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    1. Keith Freeland, R. & McCabe, Brendan, 2005. "Asymptotic properties of CLS estimators in the Poisson AR(1) model," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 147-153, June.
    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. 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.
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    Cited by:

    1. Scotto, Manuel G. & Weiß, Christian H. & Silva, Maria Eduarda & Pereira, Isabel, 2014. "Bivariate binomial autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 233-251.
    2. Simon Nik, 2024. "Marginal analysis of count time series in the presence of missing observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(4), pages 1105-1128, December.
    3. Kirchner, Matthias & Torrisi, Giovanni Luca, 2023. "Fluctuations and precise deviations of cumulative INAR time series," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 1-32.

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