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Constrained functional time series: Applications to the Italian gas market

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  • Canale, Antonio
  • Vantini, Simone

Abstract

Motivated by market dynamic modelling in the Italian Natural Gas Balancing Platform, we propose a model for analyzing time series of functions, subject to equality and inequality constraints at the two edges of the domain, respectively, such as daily demand and offer curves. Specifically, we provide the constrained functions with suitable pre-Hilbert structures, and introduce a useful isometric bijective map that associates each possible bounded and monotonic function to an unconstrained one. We introduce a functional-to-functional autoregressive model that is used to forecast future demand/offer functions, and estimate the model via the minimization of a penalized mean squared error of prediction, with a penalty term based on the Hilbert–Schmidt squared norm of autoregressive lagged operators. The approach is of general interest and could be generalized to any situation in which one has to deal with functions that are subject to the above constraints which evolve over time.

Suggested Citation

  • Canale, Antonio & Vantini, Simone, 2016. "Constrained functional time series: Applications to the Italian gas market," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1340-1351.
    • Handle: RePEc:eee:intfor:v:32:y:2016:i:4:p:1340-1351
    DOI: 10.1016/j.ijforecast.2016.05.002
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    5. Chen, Ying & Koch, Thorsten & Zakiyeva, Nazgul & Zhu, Bangzhu, 2020. "Modeling and forecasting the dynamics of the natural gas transmission network in Germany with the demand and supply balance constraint," Applied Energy, Elsevier, vol. 278(C).
    6. Centofanti, Fabio & Fontana, Matteo & Lepore, Antonio & Vantini, Simone, 2022. "Smooth LASSO estimator for the Function-on-Function linear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    7. Matteo Fontana & Massimo Tavoni & Simone Vantini, 2019. "Functional Data Analysis of high-frequency load curves reveals drivers of residential electricity consumption," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-16, June.
    8. Francisco Martínez-Álvarez & Amandine Schmutz & Gualberto Asencio-Cortés & Julien Jacques, 2018. "A Novel Hybrid Algorithm to Forecast Functional Time Series Based on Pattern Sequence Similarity with Application to Electricity Demand," Energies, MDPI, vol. 12(1), pages 1-18, December.
    9. Dominique Guégan & Matteo Iacopini, 2018. "Nonparameteric forecasting of multivariate probability density functions," Documents de travail du Centre d'Economie de la Sorbonne 18012, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    10. Kokoszka, Piotr & Miao, Hong & Petersen, Alexander & Shang, Han Lin, 2019. "Forecasting of density functions with an application to cross-sectional and intraday returns," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1304-1317.
    11. Matteo Iacopini & Dominique Guégan, 2018. "Nonparametric Forecasting of Multivariate Probability Density Functions," Working Papers 2018:15, Department of Economics, University of Venice "Ca' Foscari".
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    13. Fabio Centofanti & Antonio Lepore & Alessandra Menafoglio & Biagio Palumbo & Simone Vantini, 2023. "Adaptive smoothing spline estimator for the function-on-function linear regression model," Computational Statistics, Springer, vol. 38(1), pages 191-216, March.
    14. Agostino Torti & Alessia Pini & Simone Vantini, 2021. "Modelling time‐varying mobility flows using function‐on‐function regression: Analysis of a bike sharing system in the city of Milan," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(1), pages 226-247, January.
    15. Rossini, Jacopo & Canale, Antonio, 2019. "Quantifying prediction uncertainty for functional-and-scalar to functional autoregressive models under shape constraints," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 221-231.
    16. Wang, You & Gong, Xu, 2022. "Analyzing the difference evolution of provincial energy consumption in China using the functional data analysis method," Energy Economics, Elsevier, vol. 105(C).
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    18. Ciarreta, Aitor & Martinez, Blanca & Nasirov, Shahriyar, 2023. "Forecasting electricity prices using bid data," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1253-1271.

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