A prediction interval for a function-valued forecast model

TL;DR

This paper introduces a flexible nonparametric function-valued forecast model called KWF, which handles nonstationary series and provides simultaneous prediction intervals using bootstrap methods, connecting functional time series with econometric prediction frameworks.

Contribution

The paper proposes the KWF model for nonstationary functional time series forecasting and develops a novel bootstrap-based method for constructing simultaneous prediction intervals.

Findings

KWF effectively models nonstationary load curves.

Bootstrap pseudo predictions enable accurate prediction intervals.

Comparison shows KWF outperforms econometric alternatives.

Abstract

Starting from the information contained in the shape of the load curves, we have proposed a flexible nonparametric function-valued fore-cast 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 addi-tion, this strategy provides with a simultaneous multiple horizon pre-diction. 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 pre-diction 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 prob-ability regions. In this work we propose to obtain prediction intervals for the KWF model that are simultaneously valid for the H predic-tion horizons that corresponds with the corresponding path forecast, making a connection between functional time series and the econome-tricians' framework.