Forecasting Generalized Quantiles of Electricity Demand: A Functional Data Approach

Cabrera, Brenda López; Schulz, Franziska

doi:10.1080/01621459.2016.1219259

Cited by 33 publications

(20 citation statements)

References 39 publications

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“…Finally, after obtaining the matrix of fitting parametersˆ j of the j-th node, the predicted quantile at time N for look-ahead time h isŷ j,N +h|N = x j,N +h|N Tˆ j (5) where x j,N +h|N ∈ R n j is newly input vector of the j-th node at time N for look-ahead time h,ŷ j,N +h|N ∈ R Q is a row vector constructed by all predicted quantiles, i.e.,ŷ…”

Section: B Probabilistic Forecasting Based On Linear Quantile Regresmentioning

confidence: 99%

“…At the top level, the probabilistic forecasting can be extensively used for stochastic unit commitment, price forecasting, and electricity trading in the market [1]. At the intermediate level, the probabilistic forecasting is used to balance supply and demand in each zone [5], [6] or substation [7]. At the bottom level, prosumers can use probabilistic information to participate in energy trading and consumers can adjust electricity consumption pattern in the dynamic environment.…”

Section: Introductionmentioning

confidence: 99%

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Day-Ahead Hierarchical Probabilistic Load Forecasting With Linear Quantile Regression and Empirical Copulas

2019

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In the smart grid era, high granular data play an important role in providing an enormous amount of information for industry and commerce, both temporally and spatially. With massive data, a hierarchical structure can be constructed, containing load series at diverse levels. With the fluctuation and uncertainty of power supply and demand increasing rapidly, hierarchical probabilistic load forecasting is necessary for a hierarchy formed by power system network, which can provide comprehensive information on electricity consumption at different levels. System operators or power market participants can make coherent decisions based on coherent forecasting. The challenge for hierarchical probabilistic load forecasting is how to produce probabilistically coherent forecasts. In order to simplify the prediction procedure and improve the prediction accuracy, an effective approach that could generate probabilistically coherent forecasts for a hierarchy is introduced in this paper. The proposed methodology has three major achievements: 1) a naive multiple linear regression model is proposed for bottom-level series; 2) a novel approach of combining quantile regression and empirical copulas is proposed to estimate the joint distribution of random variables; 3) to improve the prediction accuracy, a weighted correction method based on constrained quantile regression is introduced to adjust predictive distributions at the bottom level. In case of studies, the effectiveness of our proposed method is verified by using two public datasets. Compared with four benchmarks, evaluation results show that the proposed approach makes better performance.

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Section: B Probabilistic Forecasting Based On Linear Quantile Regresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Day-Ahead Hierarchical Probabilistic Load Forecasting With Linear Quantile Regression and Empirical Copulas

2019

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“…Demand forecasts are important for various levels of aggregation of the individual consumers. For example, grid management can benefit from the availability of predictions at the level of individuals, transformers, feeders, substations, balancing areas, cities, regions, and countries (Smith et al 2010, Cho et al 2013, Haben et al 2014, Sun et al 2016, Cabrera & Schulz 2017. In this context, the forecasting problem involves a hierarchy of time series, with levels consisting of differing degrees of aggregation.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Probabilistic Forecasting of Electricity Demand With Smart Meter Data

Taieb

Taylor

Hyndman

2020

Journal of the American Statistical Association

102

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Decisions regarding the supply of electricity across a power grid must take into consideration the inherent uncertainty in demand. Optimal decision-making requires probabilistic forecasts for demand in a hierarchy with various levels of aggregation, such as substations, cities and regions. The forecasts should be coherent in the sense that the forecast of the aggregated series should equal the sum of the forecasts of the corresponding disaggregated series. Coherency is essential, since the allocation of electricity at one level of the hierarchy relies on the appropriate amount being provided from the previous level. We introduce a new probabilistic forecasting method for a large hierarchy based on UK residential smart meter data. We find our method provides coherent and accurate probabilistic forecasts, as a result of an effective forecast combination. Furthermore, by avoiding distributional assumptions, we find that our method captures the variety of distributions in the smart meter hierarchy. Finally, the results confirm that, to ensure coherency in our large-scale hierarchy, it is sufficient to model a set of lower-dimension dependencies, rather than modeling the entire joint distribution of all series in the hierarchy. In achieving coherent and accurate hierarchical probabilistic forecasts, this work contributes to improved decision-making for smart grids.

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“…However, in many applications, a mean prediction is not good enough. Full predictive distributions, also known as probabilistic forecasts, are required in applications where an assessment of the associated uncertainty is essential, for example in models of future disease progression (Küffner et al 2015), electricity demand (Cabrera and Schulz 2017), stock asset returns (Mitrodima and Griffin 2017), and counterfactual distributions (Chernozhukov et al 2013). In these applications, the prediction "takes the form of a predictive probability distribution over future quantities B Torsten Hothorn Torsten.Hothorn@uzh.ch 1 Institut für Epidemiologie, Biostatistik und Prävention, Universität Zürich, Hirschengraben 84, 8001 Zürich, Switzerland or events of interest" (Gneiting and Katzfuss 2014).…”

Section: Introductionmentioning

confidence: 99%

Transformation boosting machines

Hothorn

2019

Stat Comput

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The broad class of conditional transformation models includes interpretable and simple as well as potentially very complex models for conditional distributions. This makes conditional transformation models attractive for predictive distribution modelling, especially because models featuring interpretable parameters and black-box machines can be understood as extremes in a whole cascade of models. So far, algorithms and corresponding theory was developed for special forms of conditional transformation models only: maximum likelihood inference is available for rather simple models, there exists a tailored boosting algorithm for the estimation of additive conditional transformation models, and a special form of random forests targets the estimation of interaction models. Here, I propose boosting algorithms capable of estimating conditional transformation models of arbitrary complexity, starting from simple shift transformation models featuring linear predictors to essentially unstructured conditional transformation models allowing complex nonlinear interaction functions. A generic form of the likelihood is maximized. Thus, the novel boosting algorithms for conditional transformation models are applicable to all types of univariate response variables, including randomly censored or truncated observations.

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Forecasting Generalized Quantiles of Electricity Demand: A Functional Data Approach

Cited by 33 publications

References 39 publications

Day-Ahead Hierarchical Probabilistic Load Forecasting With Linear Quantile Regression and Empirical Copulas

Day-Ahead Hierarchical Probabilistic Load Forecasting With Linear Quantile Regression and Empirical Copulas

Hierarchical Probabilistic Forecasting of Electricity Demand With Smart Meter Data

Transformation boosting machines

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