IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2206.02376.html
   My bibliography  Save this paper

The Impact of Sampling Variability on Estimated Combinations of Distributional Forecasts

Author

Listed:
  • Ryan Zischke

    (Department of Econometrics and Business Statistics, Monash University
    Methodology Division, Australian Bureau of Statistics)

  • Gael M. Martin

    (Department of Econometrics and Business Statistics, Monash University)

  • David T. Frazier

    (Department of Econometrics and Business Statistics, Monash University)

  • D. S. Poskitt

    (Department of Econometrics and Business Statistics, Monash University)

Abstract

We investigate the performance and sampling variability of estimated forecast combinations, with particular attention given to the combination of forecast distributions. Unknown parameters in the forecast combination are optimized according to criterion functions based on proper scoring rules, which are chosen to reward the form of forecast accuracy that matters for the problem at hand, and forecast performance is measured using the out-of-sample expectation of said scoring rule. Our results provide novel insights into the behavior of estimated forecast combinations. Firstly, we show that, asymptotically, the sampling variability in the performance of standard forecast combinations is determined solely by estimation of the constituent models, with estimation of the combination weights contributing no sampling variability whatsoever, at first order. Secondly, we show that, if computationally feasible, forecast combinations produced in a single step -- in which the constituent model and combination function parameters are estimated jointly -- have superior predictive accuracy and lower sampling variability than standard forecast combinations -- where constituent model and combination function parameters are estimated in two steps. These theoretical insights are demonstrated numerically, both in simulation settings and in an extensive empirical illustration using a time series of S&P500 returns.

Suggested Citation

  • Ryan Zischke & Gael M. Martin & David T. Frazier & D. S. Poskitt, 2022. "The Impact of Sampling Variability on Estimated Combinations of Distributional Forecasts," Papers 2206.02376, arXiv.org.
  • Handle: RePEc:arx:papers:2206.02376
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2206.02376
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

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


    Cited by:

    1. Wang, Xiaoqian & Hyndman, Rob J. & Li, Feng & Kang, Yanfei, 2023. "Forecast combinations: An over 50-year review," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1518-1547.

    More about this item

    JEL classification:

    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:arx:papers:2206.02376. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.