Random Walk Forecasts of Stationary Processes Have Low Bias

Kenneth West and Kurt Lunsford

No 34112, NBER Working Papers from National Bureau of Economic Research, Inc

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.

JEL-codes: C22 C53 E37 E47 (search for similar items in EconPapers)
Date: 2025-08
New Economics Papers: this item is included in nep-ets and nep-for
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Working Paper: Random Walk Forecasts of Stationary Processes Have Low Bias (2023)
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