IDEAS home Printed from https://ideas.repec.org/p/gwc/wpaper/2008-003.html
   My bibliography  Save this paper

Exponential smoothing and non-negative data

Author

Listed:
  • Muhammad Akram

    () (Department of Econometrics and Business Statistics)

  • Rob J Hyndman

    () (Department of Econometrics and Business Statistics,Monash University)

  • J. Keith Ord

    () (McDonough School of Business,Georgetown University)

Abstract

The most common forecasting methods in business are based on exponential smoothing and the most common time series in business are inherently non-negative. Therefore it is of interest to consider the properties of the potential stochastic models underlying exponential smoothing when applied to non-negative data. We explore exponential smoothing state space models for non-negative data under various assumptions about the innovations, or error, process. We first demonstrate that prediction distributions from some commonly used state space models may have an infinite variance beyond a certain forecasting horizon. For multiplicative error models which do not have this flaw, we show that sample paths will converge almost surely to zero even when the error distribution is non-Gaussian. We propose a new model with similar properties to exponential smoothing, but which does not have these problems, and we develop some distributional properties for our new model. We then explore the implications of our results for inference, and compare the short-term forecasting performance of the various models using data on the weekly sales of over three hundred items of costume jewelry. The main findings of the research are that the Gaussian approximation is adequate for estimation and one-step-ahead forecasting. However, as the forecasting horizon increases, the approximate prediction intervals become increasingly problematic. When the model is to be used for simulation purposes, a suitably specified scheme must be employed.

Suggested Citation

  • Muhammad Akram & Rob J Hyndman & J. Keith Ord, 2008. "Exponential smoothing and non-negative data," Working Papers 2008-003, The George Washington University, Department of Economics, Research Program on Forecasting.
  • Handle: RePEc:gwc:wpaper:2008-003
    as

    Download full text from publisher

    File URL: https://www2.gwu.edu/~forcpgm/2008-003.pdf
    Download Restriction: no

    Citations

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


    Cited by:

    1. Snyder, Ralph D. & Ord, J. Keith & Beaumont, Adrian, 2012. "Forecasting the intermittent demand for slow-moving inventories: A modelling approach," International Journal of Forecasting, Elsevier, vol. 28(2), pages 485-496.
    2. Ralph D. Snyder & J. Keith Ord & Adrian Beaumont, 2010. "Forecasting the Intermittent Demand for Slow-Moving Items," Working Papers 2010-003, The George Washington University, Department of Economics, Research Program on Forecasting, revised Mar 2011.
    3. Svetunkov, Ivan & Boylan, John Edward, 2017. "Multiplicative state-space models for intermittent time series," MPRA Paper 82487, University Library of Munich, Germany.
    4. de Silva, Ashton J, 2010. "Forecasting Australian Macroeconomic variables, evaluating innovations state space approaches," MPRA Paper 27411, University Library of Munich, Germany.
    5. Alysha M De Livera, 2010. "Automatic forecasting with a modified exponential smoothing state space framework," Monash Econometrics and Business Statistics Working Papers 10/10, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    Keywords

    forecasting; time series; exponential smoothing; positive-valued processes; seasonality; state space models.;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

    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:gwc:wpaper:2008-003. 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: (Tara M. Sinclair). General contact details of provider: http://edirc.repec.org/data/degwuus.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.