Modelling and Forecasting Daily Electricity Load via Curve Linear Regression

Abstract

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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“…. ) by performing a regularized linear regression on a spline basis transfer functions (see Goude, 2011, Pierrot et al, 2009); the CLR forecaster performs a data driven dimension reduction together with a data transformation so as to reduce the problem to a simple linear regression (see Cho et al, 2013Cho et al, , 2014; the KWF is a nearest neighbors approach on a wavelet basis (see Antoniadis et al, 2006Antoniadis et al, , 2010Antoniadis et al, , 2012Antoniadis et al, , 2013. These individual forecasters were carefully chosen because they exhibit good performance and various behaviors.…”

Day-ahead probabilistic forecasting for French half-hourly electricity loads and quantiles for curve-to-curve regression

“…curve. This is the same setting as Cho et al (2013Cho et al ( , 2015. Perform the singularvalue-decomposition (SVD):…”

“…Within the context of forecasting daily loads with high temporal resolution, it is attractive to review the loads over a day as a curve. It embeds nonstationary daily patterns into a stationary framework in a Hilbert space, and, therefore, provides competitive and reliable pointwise forecasting; see Cho et al (2013Cho et al ( , 2015; Chen and Li (2017); Chen et al (2020). The goal of this paper is to develop some probabilistic predictors for curves (PPC) with a pre-specified coverage probability.…”

Probabilistic Forecasting for Daily Electricity Loads and Quantiles for Curve-to-Curve Regression

“…is zero-mean independent noise curve. This is the same setting as Cho et al (2013Cho et al ( , 2015. Perform the singularvalue-decomposition (SVD):…”