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The project that gave rise to these results received the support of a fellowship from "la Caixa" Foundation (ID 100010434). The fellowship code is LCF/BQ/DR20/11790028. This work has also been partially supported by the Spanish Ministry of Science, Innovation and Universities, Gobierno de Espana, under Contract No. PID2021-122711NB-C21 and by DG of Research and Technological Innovation of the Community of Madrid (Spain) under Contract No. IND2022/TIC-23716.

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Quantifying the Uncertainty of Reservoir Computing: Confidence Intervals for Time-Series Forecasting

Publicado en:Mathematics. 12 (19): 3078- - 2024-10-01 12(19), DOI: 10.3390/math12193078

Autores: Domingo, Laia; Grande, Mar; Borondo, Florentino; Borondo, Javier

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Resumen

Recently, reservoir computing (RC) has emerged as one of the most effective algorithms to model and forecast volatile and chaotic time series. In this paper, we aim to contribute to the understanding of the uncertainty associated with the predictions made by RC models and to propose a methodology to generate RC prediction intervals. As an illustration, we analyze the error distribution for the RC model when predicting the price time series of several agri-commodities. Results show that the error distributions are best modeled using a Normal Inverse Gaussian (NIG). In fact, NIG outperforms the Gaussian distribution, as the latter tends to overestimate the width of the confidence intervals. Hence, we propose a methodology where, in the first step, the RC generates a forecast for the time series and, in the second step, the confidence intervals are generated by combining the prediction and the fitted NIG distribution of the RC forecasting errors. Thus, by providing confidence intervals rather than single-point estimates, our approach offers a more comprehensive understanding of forecast uncertainty, enabling better risk assessment and more informed decision-making in business planning based on forecasted prices.

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