Bayesian Quantile Deep Echo State Networks for Nonlinear Time Series
Abstract
Conditional quantiles are central to asymmetric decision losses, tail-risk assessment, and interval forecasts, but Bayesian quantile regression for nonlinear time series can be difficult when the temporal feature vector is high-dimensional. We develop the quantile deep echo state network (Q-DESN), a Bayesian quantile regression model conditional on fixed features generated by a deep echo state network. Conditional on a specified reservoir construction and feature map, posterior uncertainty is assigned to the regression coefficients, likelihood, and shrinkage parameters. Single-level fits use asymmetric Laplace or quantile-fixed generalized asymmetric Laplace working likelihoods with ridge or regularized-horseshoe priors. Posterior computation uses Markov chain Monte Carlo when computationally practical and a model-specific variational Bayes approximation for analyses requiring repeated fitting. For quantile grids, we compare independent level-wise regressions followed by monotone rearrangement with a joint quantile-vector regression that shrinks adjacent quantile-specific coefficient differences. Synthetic studies, a single-origin retrospective Global Flood Awareness System (GloFAS) streamflow case, and a retrospective PriceFM comparison identify settings where this fixed-feature Bayesian regression improves finite-grid quantile scores.
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BibTeX
@misc{leon2026bayesian,
title = {{Bayesian Quantile Deep Echo State Networks for Nonlinear Time Series}},
author = {Antonio De Leon and Raquel Prado and Bruno Sansó},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17579},
eprint = {2609.17579},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17579},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bayesian Quantile Deep Echo State Networks for Nonlinear Time Series
AU - Antonio De Leon
AU - Raquel Prado
AU - Bruno Sansó
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.17579
UR - https://arxiv.org/abs/2609.17579
AB - Conditional quantiles are central to asymmetric decision losses, tail-risk assessment, and interval forecasts, but Bayesian quantile regression for nonlinear time series can be difficult when the temporal feature vector is high-dimensional. We develop the quantile deep echo state network (Q-DESN), a Bayesian quantile regression model conditional on fixed features generated by a deep echo state network. Conditional on a specified reservoir construction and feature map, posterior uncertainty is assigned to the regression coefficients, likelihood, and shrinkage parameters. Single-level fits use asymmetric Laplace or quantile-fixed generalized asymmetric Laplace working likelihoods with ridge or regularized-horseshoe priors. Posterior computation uses Markov chain Monte Carlo when computationally practical and a model-specific variational Bayes approximation for analyses requiring repeated fitting. For quantile grids, we compare independent level-wise regressions followed by monotone rearrangement with a joint quantile-vector regression that shrinks adjacent quantile-specific coefficient differences. Synthetic studies, a single-origin retrospective Global Flood Awareness System (GloFAS) streamflow case, and a retrospective PriceFM comparison identify settings where this fixed-feature Bayesian regression improves finite-grid quantile scores.
ER -