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Quantifying prediction uncertainty for functional-and-scalar to functional autoregressive models under shape constraints
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Quantifying prediction uncertainty for functional-and-scalar to functional autoregressive models under shape constraints

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  • Rossini, Jacopo
  • Canale, Antonio

Abstract

Motivated by demand and supply curve forecasting in energy markets, we discuss an autoregressive functional modeling framework that preserves curve constraints, includes exogenous scalar information, and provides prediction uncertainty quantification. The model is a functional autoregressive model that relies on a non-concurrent functional autoregressive model in a non-standard pre-Hilbert space in order to satisfy the curve constraints. Prediction uncertainty is quantified by means of a novel bootstrap approach for dependent functional data where the predictive bootstrap trajectories are represented alongside the prediction to show how forecasting confidence varies in the domain. Computational and numerical details are discussed in order to replicate the model estimation process an adequate number of times during the bootstrap phase. The method is applied to Italian natural gas market data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:170:y:2019:i:c:p:221-231
    DOI: 10.1016/j.jmva.2018.10.007
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    References listed on IDEAS

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    3. 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.
    4. Aue, Alexander & Van Delft, Anne, 2017. "Testing for stationarity of functional time series in the frequency domain," LIDAM Discussion Papers ISBA 2017001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    1. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.

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