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Half-drift forecasting for random walks
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AI
DOI：10.1093/imaman/dpaf037.png)
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Abstract
En 中文
Accepted by: Aris SyntetosWe derive a new forecast function for forecasting random walks. The resulting forecast eliminates the a priori average forecast bias and minimizes the a priori average mean squared error, the average being taken between a driftless and a drifting random walk process. We derive explicit conditions for such optimality for this new forecast, show that this is not affected by the presence of unequal variances of the corresponding data generating processes and derive the feasible forecast function, after the estimation of the drift parameter. This new forecast function takes a surprisingly simple form, that of a random walk with a half-drift, which makes the computation easy and expedient to use in any forecasting analysis. We explore the efficacy of the proposed approach in an empirical illustration and with simulations and find that, despite its obvious simplicity, the half-drift forecast often delivers lower forecast errors than the naive and naive-with-drift benchmarks in finite samples-particularly when samples are small or volatility is elevated-while remaining competitive otherwise. We also illustrate how this idea can easily be applied in a bivariate setting and how it can assist in uncovering causality in forecasting. Our theoretical and empirical results, combined with the immediate applicability of the method, recommends its immediate use in applications, as it can comfortably stand both on its own as a forecasting method and also, and possibly more importantly, as an improved and more robust forecasting benchmark.
Keywords:
average forecast
average MSE
forecast combination
half-drift
random walk
random walk with drift.
Journal
I
IF:
4.3
Papers:
27
Citations:
766