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This paper provides two procedures to obtain prediction intervals for electricity demand and price based on functional data. The proposed procedures are related to one day ahead pointwise forecast. In particular, the first method uses a nonparametric autoregressive model and the second one uses a partial linear semi-parametric model, in which exogenous scalar covariates are incorporated in a linear way. In both cases, the proposed procedures for the construction of the prediction intervals use residual-based bootstrap algorithms, which allows also to obtain estimates of the prediction density. Applications to the Spanish Electricity Market, in year 2012, are reported. This work extends and complements the results of Aneiros et al. (2016), focused on pointwise forecasts of next-day electricity demand and price daily curves.

This paper presents an application of functional additive models in the context of electricity demand and price prediction. Data from the Spanish electricity market are used to obtain the pointwise predictions. Also prediction intervals, based on a bootstrap procedure, are computed. This approach is compared with the use of other functional regression methods applied to the same data set by Aneiros et al. (2016).

This paper deals with the semi-functional partial linear regression model $$Y={{\varvec{X}}}^\mathrm{T}{\varvec{\beta }}+m({\varvec{\chi }})+\varepsilon $$ under $$\alpha $$ -mixing conditions. $${\varvec{\beta }} \in \mathbb {R}^{p}$$ and $$m(\cdot )$$ denote an unknown vector and an unknown smooth real-valued operator, respectively. The covariates $${{\varvec{X}}}$$ and $${\varvec{\chi }}$$ are valued in $$\mathbb {R}^{p}$$ and some infinite-dimensional space, respectively, and the random error $$\varepsilon $$ verifies $$\mathbb {E}(\varepsilon |{{\varvec{X}}},{\varvec{\chi }})=0$$ . Naive and wild bootstrap procedures are proposed to approximate the distribution of kernel-based estimators of $${\varvec{\beta }}$$ and $$m(\chi )$$ , and their asymptotic validities are obtained. A simulation study shows the behavior (on finite sample sizes) of the proposed bootstrap methodology when applied to construct confidence intervals, while an application to real data concerning electricity market illustrates its usefulness in practice.

This study proposes a control chart based on functional data to detect anomalies and estimate the normal output of industrial processes and services such as those related to the energy efficiency domain. Companies providing statistical consultancy services in the fields of energy efficiency, heating, ventilation and air conditioning (HVAC), installation and control, and big data for buildings, have been striving to solve the problem of automatic anomaly detection in buildings controlled by sensors. Given the functional nature of the critical to quality (CTQ) variables, this study proposed a new functional data analysis (FDA) control chart method based on the concept of data depth. Specifically, it developed a control methodology, including the Phase I and II control charts. It is based on the calculation of the depth of functional data, the identification of outliers by smooth bootstrap resampling and the customization of nonparametric rank control charts. A comprehensive simulation study, comprising scenarios defined with different degrees of dependence between curves, was conducted to evaluate the control procedure. The proposed statistical process control procedure was also applied to detect energy efficiency anomalies in the stores of a textile company in the Panama City. In this case, energy consumption has been defined as the CTQ variable of the HVAC system. Briefly, the proposed methodology, which combines FDA and multivariate techniques, adapts the concept of the control chart based on a specific case of functional data and thereby presents a novel alternative for controlling facilities in which the data are obtained by continuous monitoring, as is the case with a great deal of process in the framework of Industry 4.0.

The features of the electricity, as well as the rules of the competitive electricity markets, create the need of accurate predictions of electricity demand and price in order to anticipate decisions. Mainly, the prediction task in energy markets has been studied in the literature with the aim of obtaining scalar (hourly, daily, …) forecasts given scalar (and/or, less frequently, functional) historical data. This paper provides two methods to predict next-day electricity demand and price daily curves given information from past curves. They are based on using robust functional principal component analysis and nonparametric models with functional both response and covariate. In addition, the nonparametric proposal is extended to incorporate, in a linear way, exogenous scalar covariates. Results of these methods for the electricity market of mainland Spain, in year 2012, are reported. Their accuracy is compared with that of a naive method as well as with the corresponding to combining forecasts. Scalar versions are also included in the comparative study. This work extends and complements the methods and results in Vilar et al. (2012), focused on scalar forecasts.

This paper considers naive and wild bootstrap procedures to construct pointwise confidence intervals for a nonparametric regression function when the predictor is of functional nature and when the data are dependent. Assuming $\alpha$-mixing conditions on the sample, the asymptotic validity of both procedures is obtained. A simulation study shows promising results when finite sample sizes are used, while an application to electricity demand data illustrates its usefulness in practice.