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Optimal Probabilistic Forecasts for Counts

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  • Brendan P.M. McCabe
  • Gael M. Martin

    ()

  • David Harris

Abstract

Optimal probabilistic forecasts of integer-valued random variables are derived. The optimality is achieved by estimating the forecast distribution nonparametrically over a given broad model class and proving asymptotic efficiency in that setting. The ideas are demonstrated within the context of the integer autoregressive class of models, which is a suitable class for any count data that can be interpreted as a queue, stock, birth and death process or branching process. The theoretical proofs of asymptotic optimality are supplemented by simulation results which demonstrate the overall superiority of the nonparametric method relative to a misspecified parametric maximum likelihood estimator, in large but .nite samples. The method is applied to counts of wage claim benefits, stock market iceberg orders and civilian deaths in Iraq, with bootstrap methods used to quantify sampling variation in the estimated forecast distributions.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2009/wp7-09.pdf
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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 7/09.

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Length: 41 pages
Date of creation: Aug 2009
Date of revision:
Handle: RePEc:msh:ebswps:2009-7

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Related research

Keywords: Nonparametric Inference; Asymptotic Efficiency; Count Time Series; INAR Model Class; Bootstrap Distributions; Iceberg Stock Market Orders.;

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Cited by:
  1. Dag Tjøstheim, 2012. "Some recent theory for autoregressive count time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 21(3), pages 413-438, September.
  2. Yousung Park & Hee-Young Kim, 2012. "Diagnostic checks for integer-valued autoregressive models using expected residuals," Statistical Papers, Springer, vol. 53(4), pages 951-970, November.

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