A prediction interval for a function-valued forecast model: Application to load forecasting

Starting from the information contained in the shape of the load curves, we propose a flexible nonparametric function-valued forecast model called KWF (Kernel + Wavelet + Functional) that is well suited to the handling of nonstationary series. The predictor can be seen as a weighted average of the futures of past situations, where the weights increase with the similarity between the past situations and the actual one. In addition, this strategy also provides simultaneous predictions at multiple horizons. These weights induce a probability distribution that can be used to produce bootstrap pseudo predictions. Prediction intervals are then constructed after obtaining the corresponding bootstrap pseudo prediction residuals. We develop two propositions following the KWF strategy directly, and compare it to two alternative methods that arise from proposals by econometricians. The latter involve the construction of 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 by bootstrapping joint probability regions. In this work, we propose to obtain prediction intervals for the KWF model that are valid simultaneously for the H prediction horizons that correspond to the relevant path forecasts, making a connection between functional time series and the econometricians' framework.