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Fully observed INAR(1) processes

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  • Christian H. Weiß

Abstract

The innovations of an INAR(1) process ( in teger-valued a uto r egressive) are usually assumed to be unobservable. There are, however, situations in practice, where also the innovations can be uncovered, i.e. where we are concerned with a fully observed INAR ( 1 ) process . We analyze stochastic properties of such a fully observed INAR(1) process and explore the relation between the INAR(1) model and certain metapopulation models. We show how the additional knowledge about the innovations can be used for parameter estimation, for model diagnostics, and for forecasting. Our findings are illustrated with two real-data examples.

Suggested Citation

  • Christian H. Weiß, 2012. "Fully observed INAR(1) processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(3), pages 581-598, July.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:3:p:581-598
    DOI: 10.1080/02664763.2011.604308
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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. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 319-341, August.
    3. R. K. Freeland & B. P. M. McCabe, 2004. "Analysis of low count time series data by poisson autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 701-722, September.
    4. Maria Eduarda Da Silva & Vera Lúcia Oliveira, 2004. "Difference Equations for the Higher‐Order Moments and Cumulants of the INAR(1) Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 317-333, May.
    5. 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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