IDEAS home Printed from https://ideas.repec.org/p/msh/ebswps/2009-7.html
   My bibliography  Save this paper

Optimal Probabilistic Forecasts for Counts

Author

Listed:
  • 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.

Suggested Citation

  • Brendan P.M. McCabe & Gael M. Martin & David Harris, 2009. "Optimal Probabilistic Forecasts for Counts," Monash Econometrics and Business Statistics Working Papers 7/09, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2009-7
    as

    Download full text from publisher

    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2009/wp7-09.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Hyndman, Rob J. & Khandakar, Yeasmin, 2008. "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i03).
    2. Shang, Han Lin & Hyndman, Rob.J., 2011. "Nonparametric time series forecasting with dynamic updating," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1310-1324.
    3. Hyndman, Rob J. & Koehler, Anne B. & Snyder, Ralph D. & Grose, Simone, 2002. "A state space framework for automatic forecasting using exponential smoothing methods," International Journal of Forecasting, Elsevier, vol. 18(3), pages 439-454.
    4. Preda, C. & Saporta, G., 2005. "Clusterwise PLS regression on a stochastic process," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 99-108, April.
    5. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-144, April.
    6. Philippe C. Besse, 2000. "Autoregressive Forecasting of Some Functional Climatic Variations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 673-687.
    7. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, December.
    8. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
    9. Reiss, Philip T. & Ogden, R. Todd, 2007. "Functional Principal Component Regression and Functional Partial Least Squares," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 984-996, September.
    10. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-135, April.
    11. Peter Hall & Mohammad Hosseini-Nasab, 2006. "On properties of functional principal components analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 109-126.
    12. Preda, C. & Saporta, G., 2005. "PLS regression on a stochastic process," Computational Statistics & Data Analysis, Elsevier, vol. 48(1), pages 149-158, January.
    13. Antoniadis, Anestis & Sapatinas, Theofanis, 2003. "Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 133-158, October.
    14. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    15. Hyndman, Rob J. & Booth, Heather, 2008. "Stochastic population forecasts using functional data models for mortality, fertility and migration," International Journal of Forecasting, Elsevier, pages 323-342.
    16. Haipeng Shen & Jianhua Z. Huang, 2008. "Interday Forecasting and Intraday Updating of Call Center Arrivals," Manufacturing & Service Operations Management, INFORMS, vol. 10(3), pages 391-410, July.
    17. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Barczy, M. & Ispány, M. & Pap, G., 2011. "Asymptotic behavior of unstable INAR(p) processes," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 583-608, March.
    2. 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;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 413-438, September.
    3. 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.

    More about this item

    Keywords

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

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:msh:ebswps:2009-7. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dr Xibin Zhang). General contact details of provider: http://edirc.repec.org/data/dxmonau.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.