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Evaluating Approximate Point Forecasting of Count Processes

Author

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  • Annika Homburg

    (Department of Mathematics and Statistics, Helmut Schmidt University, 22043 Hamburg, Germany)

  • Christian H. Weiß

    (Department of Mathematics and Statistics, Helmut Schmidt University, 22043 Hamburg, Germany)

  • Layth C. Alwan

    (Sheldon B. Lubar School of Business, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA)

  • Gabriel Frahm

    (Department of Mathematics and Statistics, Helmut Schmidt University, 22043 Hamburg, Germany)

  • Rainer Göb

    (Institute of Mathematics, Department of Statistics, University of Würzburg, 97070 Würzburg, Germany)

Abstract

In forecasting count processes, practitioners often ignore the discreteness of counts and compute forecasts based on Gaussian approximations instead. For both central and non-central point forecasts, and for various types of count processes, the performance of such approximate point forecasts is analyzed. The considered data-generating processes include different autoregressive schemes with varying model orders, count models with overdispersion or zero inflation, counts with a bounded range, and counts exhibiting trend or seasonality. We conclude that Gaussian forecast approximations should be avoided.

Suggested Citation

  • Annika Homburg & Christian H. Weiß & Layth C. Alwan & Gabriel Frahm & Rainer Göb, 2019. "Evaluating Approximate Point Forecasting of Count Processes," Econometrics, MDPI, vol. 7(3), pages 1-28, July.
    • Handle: RePEc:gam:jecnmx:v:7:y:2019:i:3:p:30-:d:246272
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    References listed on IDEAS

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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. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(6), pages 808-817, December.
    3. Brendan P. M. McCabe & Gael M. Martin & David Harris, 2011. "Efficient probabilistic forecasts for counts," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 253-272, March.
    4. Darryll Hendricks, 1996. "Evaluation of value-at-risk models using historical data," Proceedings 512, Federal Reserve Bank of Chicago.
    5. Gneiting, Tilmann, 2011. "Quantiles as optimal point forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 197-207.
    6. Du Jin‐Guan & Li Yuan, 1991. "THE INTEGER‐VALUED AUTOREGRESSIVE (INAR(p)) MODEL," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(2), pages 129-142, March.
    7. Raju Maiti & Atanu Biswas & Samarjit Das, 2016. "Coherent forecasting for count time series using Box–Jenkins's AR(p) model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(2), pages 123-145, May.
    8. Christian H. Weiß & Philip K. Pollett, 2014. "Binomial Autoregressive Processes With Density-Dependent Thinning," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 115-132, March.
    9. 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.
    10. Layth C. Alwan & Christian H. Weiß, 2017. "INAR implementation of newsvendor model for serially dependent demand counts," International Journal of Production Research, Taylor & Francis Journals, vol. 55(4), pages 1085-1099, February.
    11. Gneiting, Tilmann, 2011. "Quantiles as optimal point forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 197-207, April.
    12. Mansour Aghababaei Jazi & Geoff Jones & Chin-Diew Lai, 2012. "First-order integer valued AR processes with zero inflated poisson innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(6), pages 954-963, November.
    13. Jung, Robert C. & Tremayne, A.R., 2006. "Coherent forecasting in integer time series models," International Journal of Forecasting, Elsevier, vol. 22(2), pages 223-238.
    14. Darryll Hendricks, 1996. "Evaluation of value-at-risk models using historical data," Economic Policy Review, Federal Reserve Bank of New York, vol. 2(Apr), pages 39-69.
    15. Luisa Bisaglia & Margherita Gerolimetto, 2015. "Forecasting integer autoregressive processes of order 1: are simple AR competitive?," Economics Bulletin, AccessEcon, vol. 35(3), pages 1652-1660.
    16. Bisaglia, Luisa & Canale, Antonio, 2016. "Bayesian nonparametric forecasting for INAR models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 70-78.
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    Cited by:

    1. Annika Homburg & Christian H. Weiß & Gabriel Frahm & Layth C. Alwan & Rainer Göb, 2021. "Analysis and Forecasting of Risk in Count Processes," JRFM, MDPI, vol. 14(4), pages 1-25, April.
    2. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    3. Kachour Maher & Bakouch Hassan S. & Mohammadi Zohreh, 2023. "A New INAR(1) Model for ℤ-Valued Time Series Using the Relative Binomial Thinning Operator," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 243(2), pages 125-152, April.
    4. Annika Homburg & Christian H. Weiß & Layth C. Alwan & Gabriel Frahm & Rainer Göb, 2021. "A performance analysis of prediction intervals for count time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(4), pages 603-625, July.
    5. Simon Nik & Christian H. Weiß, 2020. "CLAR(1) point forecasting under estimation uncertainty," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(4), pages 489-516, November.
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