Abstract
In this papers we examine the relative increase in mean square forecast error from fitting a weakly stationary process to the series of interest when in fact the true model is a so-called perturbed long-memory process recently introduced by Granger and Marmol (1997). This model has the property of being unidentifiable from a white noise process on the basis of the correlogram and the usual rule-of-thumbs in the Box-Jenkins methodology. We prove that this kind of misspecification can lead to serious errors in terms of forecasting. We also show that corrections based on the AR(1) model can in some cases partially solve the problem.
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Arranz, M.A., Marmol, F. Out-of-sample forecast errors in misspecific perturbed long memory processes. Statistical Papers 42, 423–436 (2001). https://doi.org/10.1007/s003620100071
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DOI: https://doi.org/10.1007/s003620100071