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Coherent Predictions of Low Count Time Series

  • B.P.M. McCabe
  • G.M. Martin

    ()

The application of traditional forecasting methods to discrete count data yields forecasts that are non-coherent. That is, such methods produce non-integer point and interval predictions which violate the restrictions on the sample space of the integer variable. This paper presents a methodology for producing coherent forecasts of low count time series. The forecasts are based on estimates of the p-step ahead predictive mass functions for a family of distributions nested in the integer-valued first-order autoregressive (INAR(1)) class. The predictive mass functions are constructed from convolutions of the unobserved components of the model, with uncertainty associated with both parameter values and model specifcation fully incorporated. The methodology is used to analyse two sets of Canadian wage loss claims data.

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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 8/03.

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Length: 28 pages
Date of creation: Apr 2003
Date of revision:
Handle: RePEc:msh:ebswps:2003-8
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  1. Chib, Siddhartha & Winkelmann, Rainer, 2001. "Markov Chain Monte Carlo Analysis of Correlated Count Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 428-35, October.
  2. Kleibergen, Frank, 2004. "Invariant Bayesian inference in regression models that is robust against the Jeffreys-Lindley's paradox," Journal of Econometrics, Elsevier, vol. 123(2), pages 227-258, December.
  3. Robert C. Jung & A. R. Tremayne, 2003. "Testing for serial dependence in time series models of counts," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 65-84, 01.
  4. 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.
  5. Chib, Siddhartha & Greenberg, Edward & Winkelmann, Rainer, 1998. "Posterior simulation and Bayes factors in panel count data models," Journal of Econometrics, Elsevier, vol. 86(1), pages 33-54, June.
  6. 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, 09.
  7. Durbin, J. & Koopman, S.J.M., 1998. "Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives," Discussion Paper 1998-142, Tilburg University, Center for Economic Research.
  8. Ray, W. D., 1997. "Hidden Markov and other models for discrete-valued time series : by Iain L. Mac Donald and Walter Zucchini. ISBN 0 412 55850 5. Monographs on Statistics and Applied Probability 70. Chapman and Hall, L," International Journal of Forecasting, Elsevier, vol. 13(4), pages 587-588, December.
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