We propose a hybrid approach for the modelling and the short-term forecasting of electricity loads. Two building blocks of our approach are (i) modelling the overall trend and seasonality by fitting a generalised additive model to the weekly averages of the load, and (ii) modelling the dependence structure across consecutive daily loads via curve linear regression. For the latter, a new methodology is proposed for linear regression with both curve response and curve regressors.The key idea behind the proposed methodology is the dimension reduction based on a singular value decomposition in a Hilbert space, which reduces the curve regression problem to several ordinary (i.e. scalar) linear regression problems.We illustrate the hybrid method using the French electricity loads between 1996 and 2009, on which we also compare our method with other available models including the EDF operational model.

We present two methods for detecting patterns and clusters in high dimensional time-dependent functional data. Our methods are based on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant local time and scale features. The multiresolution aspect of the wavelet transform provides a time-scale decomposition of the signals allowing to visualize and to cluster the functional data into homogeneous groups. For each input function, through its empirical orthogonal wavelet transform the first method uses the distribution of energy across scales generate a handy number of features that can be sufficient to still make the signals well distinguishable. Our new similarity measure combined with an efficient feature selection technique in the wavelet domain is then used within more or less classical clustering algorithms to effectively differentiate among high dimensional populations. The second method uses dissimilarity measures between the whole time-scale representations and are based on wavelet-coherence tools. The clustering is then performed using a k-centroid algorithm starting from these dissimilarities. Practical performance of these methods that jointly designs both the feature selection in the wavelet domain and the classification distance is demonstrated through simulations as well as daily profiles of the French electricity power demand.

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.

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Modelling and forecasting daily electricity load via curve linear regressionHaeran Cho, Yannig Goude, Xavier Brossat and Qiwei Yao Abstract In this paper, we discuss the problem of short-term electricity load forecasting by regarding electricity load on each day as a curve. The dependence between successive daily loads and other relevant factors such as temperature, is modelled via curve linear regression where both the response and the regressor are functional (curves). The key ingredient of the proposed method is the dimension reduction based on the singular value decomposition in a Hilbert space, which reduces the curve linear regression problem to several ordinary (i.e. scalar) linear regression problems. This method has previously been adopted in the hybrid approach proposed by [6] for the same purpose, where the curve linear regression modelling was applied to the data after the trend and the seasonality were removed by a generalised additive model fitted at the weekly level. We show that classifying the successive daily loads prior to curve linear regression removes the necessity of such a two-stage approach as well as resulting in reducing the forecasting error by a great margin. The proposed methodology is illustrated using the electricity load dataset collected between 2007 and mid-2012, on which it is compared to the hybrid approach and other available competitors. Finally, various ways for improving the forecasting performance of the curve linear regression technique are discussed.

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