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A review study of functional autoregressive models with application to energy forecasting

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Abstract In this data‐rich era, it is essential to develop advanced techniques to analyze and understand large amounts of data and extract the underlying information in a flexible way. We provide a review study on the state‐of‐the‐art statistical time series models for univariate and multivariate functional data with serial dependence. In particular, we review functional autoregressive (FAR) models and their variations under different scenarios. The models include the classic FAR model under stationarity; the FARX and pFAR model dealing with multiple exogenous functional variables and large‐scale mixed‐type exogenous variables; the vector FAR model and common functional principal component technique to handle multiple dimensional functional time series; and the warping FAR, varying coefficient‐FAR and adaptive FAR models to handle seasonal variations, slow varying effects and the more challenging cases of structural changes or breaks respectively. We present the models’ setup and detail the estimation procedure. We discuss the models’ applicability and illustrate the numerical performance using real‐world data of high‐resolution natural gas flows in the high‐pressure gas pipeline network of Germany. We conduct 1‐day and 14‐days‐ahead out‐of‐sample forecasts of the daily gas flow curves. We observe that the functional time series models generally produce stable out‐of‐sample forecast accuracy. This article is categorized under: Statistical Models > Semiparametric Models Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
Daily gas flow curves at two representative nodes from 1 October Y1 to 30 September Y3
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Exogenous scalar variables: four prices, that is, NCG, GASPOOL, TTF, and Zeebruegge; three renewable energy sources, that is, solar, wind‐onshore and wind‐offshore, and average temperature of four zones from 1 October Y1 to 30 September Y3, where Y1 and Y3 denote the years
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Sample autocorrelations of the gas flows at 9 a.m. and sample cross‐correlations surfaces of gas flows among 24 hr at M1 and M2 from 1 October Y1 to 30 September Y3
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Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
Statistical Models > Semiparametric Models

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