A prediction interval for a function-valued forecast model
Résumé
Starting from the information contained in the shape of the load curves, we have proposed a flexible nonparametric function-valued forecast model called KWF (Kernel+Wavelet+Functional) well suited to handle nonstationary series. The predictor can be seen as a weighted average of futures of past situations, where the weights increase with the similarity between the past situations and the actual one. In addition, this strategy provides with a simultaneous multiple horizon prediction. These weights induce a probability distribution that can be used to produce bootstrap pseudo predictions. Prediction intervals are constructed after obtaining the corresponding bootstrap pseudo prediction residuals. We develop two propositions following directly the KWF strategy and compare it to two alternative ways coming from proposals of econometricians. They construct simultaneous prediction intervals using multiple comparison corrections through the control of the family wise error (FWE) or the false discovery rate. Alternatively, such prediction intervals can be constructed bootstrapping joint probability regions. In this work we propose to obtain prediction intervals for the KWF model that are simultaneously valid for the H prediction horizons that corresponds with the corresponding path forecast, making a connection between functional time series and the econometricians' framework.
Domaines
Statistiques [math.ST]Origine | Fichiers produits par l'(les) auteur(s) |
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