IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/34112.html

Random Walk Forecasts of Stationary Processes Have Low Bias

Author

Listed:
  • Kenneth D. West
  • Kurt G. Lunsford

Abstract

We study the use of a misspecified overdifferenced model to forecast the level of a stationary scalar time series. Let x(t) be the series, and let bias be the sample average of a series of forecast errors. Then, the bias of forecasts of x(t) generated by a misspecified overdifferenced ARMA model for Δx(t) will tend to be smaller in magnitude than the bias of forecasts of x(t) generated by a correctly specified model for x(t). Formally, let P be the number of forecasts. The bias from the model for Δx(t) has a variance that is O(1/P^2), while the variance of the bias from the model for x(t) generally is O(1/P). With a driftless random walk as our baseline overdifferenced model, we confirm this theoretical result with simulations and empirical work: random walk bias is generally one-tenth to one-half that of an appropriately specified model fit to levels.

Suggested Citation

  • Kenneth D. West & Kurt G. Lunsford, 2025. "Random Walk Forecasts of Stationary Processes Have Low Bias," NBER Working Papers 34112, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:34112
    Note: AP EFG IFM ME TWP
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w34112.pdf
    Download Restriction: Access to the full text is generally limited to series subscribers, however if the top level domain of the client browser is in a developing country or transition economy free access is provided. More information about subscriptions and free access is available at http://www.nber.org/wwphelp.html. Free access is also available to older working papers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or

    for a different version of it.

    Other versions of this item:

    More about this item

    JEL classification:

    • 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
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications

    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:nbr:nberwo:34112. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    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.