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

Abstract

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.

Modeling public holidays in load forecasting: a German case study

“…In some studies [19][20][21][22][23] unwanted holidays are removed (or excluded) from the underlying data set, or they are treated as missing data. In contrast to the ignoring the public holidays approach we have the advantage of not having the public holiday bias for the training or estimation.…”

“…To define these out-of-sample day subsets O, let Oos be the set of all out-of-sample days; here 5 years from January 2012 to December 2016. Then, we consider in total five options for the subset O: The scores defined by (19) and (20) allow the comparison of prediction methods. However, just reporting the out-of-sample MAE or RMSE does not directly allow significance statements.…”

Electricity Demand Forecasting: The Uruguayan Case

“…Non stationary patterns are treated by means of corrections applied on the wavelet coefficients (see Antoniadis et al [2012] for details). Prediction intervals can be obtained using a bootstrap strategy where the bootstrap sampling is determined by {w m,n } the weight vector (see Antoniadis et al [2016]).…”

Prediction Interval Construction for Byproduct Gas Flow Forecasting Using Optimized Twin Extreme Learning Machine

“…The main idea behind the method is to construct lower and upper bounds of PIs directly by optimizing the coefficients of the NN according to the interval quality evaluation indices. Because it offers good performance and does not require strict data distribution assumptions, the LUBE method has been widely used in many real-world problems, such as bus travel time prediction [20], electrical load forecasting [21,22], and Landslide displacement prediction [23]. However, conventional NNs employed in the LUBE method suffer from the problems of overtraining and a high computational burden.…”

“…However, when using NNs to perform interval forecasting, the initial values of the connection weights are usually generated randomly [19][20][21][22]. The effects of connection weight initialization on the final constructed PIs are usually ignored.…”