Pith. sign in

REVIEW 4 major objections 5 minor 1 cited by

Quantile deep learning models for multi-step ahead time series prediction

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Swapping the loss function of LSTM and CNN forecasters for quantile loss yields interval predictions without sacrificing point accuracy.

desk verdict Plausible internal comparison but the random 80:20 split leaks future information, so the headline forecasting claim is not yet supported; a temporal re-split and quantile calibration check could fix it. read the letter →

arxiv 2411.15674 v1 pith:5ZTYW74G submitted 2024-11-24 cs.LG cs.AIq-fin.STstat.ME

Jimmy Cheung , Smruthi Rangarajan , Amelia Maddocks , Xizhe Chen , Rohitash Chandra This is my paper · ORCID
classification cs.LGcs.AIq-fin.STstat.ME
keywords quantileregressiondeeplearningtimeseriespredictionmulti-stepaheaduncertaintyquantificationcryptocurrencyLSTMCNN
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to show that adding quantile regression to standard deep learning forecasters produces multi-step ahead predictions with uncertainty intervals at no cost in point accuracy. The authors build quantile versions of bidirectional, encoder-decoder, and convolutional LSTM models, trained with the asymmetric check loss instead of mean squared error, and test them on Bitcoin, Ethereum, and three benchmark time series. They report that the quantile models match and sometimes beat their conventional counterparts, and that the median output of a quantile ED-LSTM is the most accurate and stable predictor. If true, this means practitioners can get calibrated-looking risk bands from the same architectures they already use, without a separate uncertainty model.

What carries the argument

The central object is the quantile (check) loss function $\rho_\tau(u) = u(\tau - \mathbb{1}_{u<0})$, applied to the output layer of standard recurrent and convolutional architectures. For each prediction horizon the network emits one value per target quantile (0.05, 0.25, 0.5, 0.75, 0.95), and the median ($\tau = 0.5$) is used as the point forecast. The loss rewards under-prediction for high $\tau$ and over-prediction for low $\tau$, so the trained network's outputs spread into a conditional quantile band. This machinery is what carries the claim: it converts a single-output forecaster into a multi-quantile forecaster with no architectural change beyond the loss and output dimension.

What would settle it

Re-run the same models with a strict chronological split (train on the earliest 80% of dates, test on the most recent 20%), keep all other hyperparameters fixed, and compare the quantile models' median RMSE and their 90% interval coverage to the baselines. If the quantile models no longer match the baselines, or if coverage falls far below 90%, the paper's central claim would be contradicted.

Watch

Extended reading notes

Core claim

The central claim is that integrating a quantile loss function with deep learning provides additional predictions for selected quantiles without a loss in prediction accuracy compared to conventional deep learning models, and that the resulting quantile models handle volatility more effectively. On Bitcoin and Ethereum daily close prices, the quantile encoder-decoder LSTM achieves the best or tied-best mean RMSE across five-step horizons, while also emitting 5th, 25th, 75th, and 95th percentile trajectories. The paper's stated objective is not to beat the existing models but to show that the quantile versions can provide uncertainty information 'for free' — matching point accuracy while adding a distributional view. The authors frame this as a form of extreme-value forecasting because the outer quantiles bound the range of possible outcomes.

Load-bearing premise

The load-bearing premise is that a randomly selected 80:20 split of a time series produces a valid test set for multi-step ahead forecasting; because training samples can come from after the test period, the reported RMSE measures interpolation within the same time span rather than genuine forward prediction.

Editorial extensions

If this is right

  • Quantile loss can be dropped into BD-LSTM, Conv-LSTM, and ED-LSTM forecasters to produce 5th–95th percentile prediction bands while keeping point RMSE effectively unchanged.
  • The median output of the quantile ED-LSTM is the most accurate and stable predictor on the cryptocurrency datasets and benchmarks tested.
  • The framework offers a simple frequentist route to uncertainty quantification in multi-step ahead forecasting, complementing Bayesian neural networks.
  • Practitioners in volatile domains such as crypto trading can obtain risk ranges directly from a single trained network instead of running ensemble or Bayesian methods.
  • The ranking across architectures (ED-LSTM best, BD-LSTM least robust) persists in the quantile versions, suggesting architecture choice dominates loss-function choice.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A chronological train/test split would likely be a stricter test; given the paper's random split, the reported RMSEs likely mix interpolation and extrapolation, so the parity claim may not survive out-of-sample.
  • The paper does not measure quantile calibration (e.g., empirical coverage of the 90% interval); a coverage check on a temporal holdout would directly test whether the bands are trustworthy.
  • The volatility-handling claim rests on tighter confidence intervals across runs; a sharper test would compare quantile-model errors during known high-volatility subperiods against baseline errors.
  • The framework extends naturally to data imputation and climate extremes, as the authors note, but those uses would require enforcing non-negativity constraints the paper admits it omitted.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper introduces quantile-regression variants of BD-LSTM, ED-LSTM, and Conv-LSTM for multi-step ahead time series prediction, replacing the standard loss with the quantile check loss and reporting RMSE at five quantiles (0.05, 0.25, 0.5, 0.75, 0.95). The models are evaluated on Bitcoin, Ethereum, Sunspot, Mackey-Glass, and Lorenz datasets, with univariate and multivariate input strategies. The central claims are that integrating a quantile loss function with deep learning provides additional quantile predictions without a loss in point-forecast accuracy relative to conventional models, and that the quantile models handle volatility more effectively.

Significance. If fully supported, the paper would provide a practical recipe for adding quantile outputs to standard deep forecasting models at negligible cost, with useful open-source code, reproducible 30-run experiments, and direct comparisons across several architectures. The accuracy-parity result is encouraging and the paper is clearly written in terms of model variants and loss functions. However, the current evaluation protocol measures interpolation on a randomly shuffled window pool rather than genuine multi-step ahead forecasting, and the absence of any probabilistic calibration metric leaves the central uncertainty-quantification claim undemonstrated. The paper also contains apparent data inconsistencies in the Ethereum tables that must be resolved before the empirical conclusions can be accepted.

major comments (4)
  1. [Section 3.5] The random 80:20 train-test split described in Section 3.5 leaks future information into the training set. Because the data are first converted into overlapping windows with input length d=6 and output length m=5 (Section 3.3), a random split of these windows places post-test observations in training and pre-test observations in testing. The reported RMSE values in Tables 2, 4, and 6 are therefore interpolation errors on a shuffled window pool, not errors of genuine multi-step-ahead forecasting. This also explains, rather than validates, the claimed volatility robustness: Section 3.5 explicitly randomizes so that COVID-era volatility appears in both training and test sets. The accuracy-parity claim and the volatility-handling claim should be re-evaluated with a temporal split (for example, the last 20% of the series as test) and with volatility-period-specific metrics.
  2. [Section 5] The comparison with Wu et al. [44] is not controlled. The paper contrasts the multivariate Quantile-ED-LSTM Bitcoin RMSE of 0.0112 with the 0.0373 reported by Wu et al. and attributes the difference to the 80:20 versus 70:30 split ratio. However, the two studies also differ in split mechanics (random window split versus the procedure used in [44]), in test-set composition, and potentially in preprocessing and hyperparameters, even though Section 3.3 relies on [44] for hyperparameters. The 0.0112 figure is itself produced under the leaking random split of the previous comment. This comparison should be removed or replaced with a head-to-head evaluation on identical temporal splits and preprocessing.
  3. [Tables 4 and 5] The Ethereum results contain apparent data errors. The multivariate ED-LSTM row in Table 4 (mean 0.0113; steps 0.0101, 0.0112, 0.0118, 0.0119, 0.0117) is identical to the multivariate ED-LSTM row for Bitcoin in Table 2, which is implausible for a different dataset. In addition, Table 5 reports a 0.5-quantile RMSE of 0.0137 for multivariate Quantile-ED-LSTM on Ethereum, whereas Table 4 reports a mean RMSE of 0.0126 for the same model and strategy; these two numbers should coincide because Section 3.2 states the median quantile is taken as the point prediction. The Ethereum-based conclusions in Section 4.1 and the rankings in Table 7 should be rechecked after correcting these entries.
  4. [Section 5 (Discussion)] The authors concede that 'We had no indication on how accurate our quantile predictions are.' Indeed, the paper never reports calibration, empirical coverage, pinball score, or quantile-crossing diagnostics for the estimated 5%-95% intervals; Tables 3 and 5 only report RMSE per quantile, which is not a proper scoring rule for distributional forecasts. Consequently, the Abstract's claim that the quantile model 'has the ability to handle volatility more effectively' is unsupported on its own terms, independent of the data-splitting issue. The paper should add proper probabilistic forecast evaluation (e.g., empirical coverage of the 5%-95% interval, interval score or pinball loss, and a high-volatility-period subsample analysis).
minor comments (5)
  1. [Section 2.1, Eq. (2)] Equation (2) appears to contain a typesetting error: the indicator function is written as '1u<0' without an explicit I(·), and the parentheses in ρτ(u) = u(τ− 1u<0)) are unbalanced.
  2. [Sections 2.1 and 3.2] The quantile notation is inconsistent: Section 2.1 uses τ, while Eq. (3) in Section 3.2 uses q; please unify the symbols.
  3. [Section 3.5] The sentence 'we use 64 filters with a kernel size of 2' appears twice in the same paragraph; please remove the duplicate.
  4. [Figure 3 caption] The caption contains the typo 'not explicitly suing in the recurrent neural network' instead of 'not explicitly shown in the recurrent neural network.'
  5. [Table 6] Table 6 reports only steps 2, 5, 8, and 10 despite the text describing 10-step horizons; please clarify whether these are representative steps and why intermediate steps are omitted.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: quantile-loss extension is tested against paired classic baselines under identical settings; the central claim does not reduce to its inputs.

full rationale

The paper's central claim—that adding quantile (pinball) loss to LSTM/CNN forecasters yields multi-quantile outputs without degrading point accuracy—is evaluated empirically by paired comparisons: each quantile model is compared with its classic counterpart trained under the same architectures, window sizes, and hyperparameters (Tables 2, 4, 6). No equation in the derivation defines the claimed output in terms of the input: the median-quantile prediction is used as the point forecast by assumption, but its RMSE is measured against held-out data rather than constructed from the training loss. The paper's self-citations ([44], [47], both from the same group) supply hyperparameters and baseline architectures, but they are not load-bearing for the central claim because the classic-vs-quantile contrast is internal and controlled under identical settings. The random 80:20 split in Section 3.5 is a genuine evaluation-validity concern: overlapping windows plus a random split mix future information into training, so the reported RMSEs measure interpolation rather than genuine multi-step out-of-sample forecasting, and the comparison with Wu et al. [44] is uncontrolled. This is a correctness risk, not circularity, because it does not make the quantile results equivalent to the inputs by construction. The Discussion's admission that 'we had no indication on how accurate our quantile predictions are' concedes missing calibration/coverage evaluation, again an evidential gap rather than a circular derivation. Overall, no step reduces to its own inputs.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claims rest on standard quantile regression theory plus several modeling choices. The most consequential is the random split, which is an ad hoc assumption that undermines the forecasting evaluation. No new entities are introduced.

free parameters (4)
  • quantile set = {0.05, 0.25, 0.5, 0.75, 0.95}
    Chosen by hand in Section 3.2 to capture uncertainty; other values are possible.
  • train-test split ratio = 80:20 random split
    Chosen in Section 3.5 to include volatile periods in training; creates temporal leakage for time series.
  • input/output window sizes = d=6 (input), m=5 (output) for crypto; d=5, m=10 for benchmarks
    Taken from Wu et al. [44] and Chandra et al. [47] rather than tuned.
  • network hyperparameters = learning rate 1e-4; hidden sizes 50/100/20; Conv filters 64, kernel 2
    Adopted from prior literature [47,44] per Table 1 and Section 3.5.
assumptions (4)
  • standard math Minimizing the quantile check loss (Eq. 3) yields consistent estimates of conditional quantiles.
    Invoked in Section 3.2; standard quantile regression theory from Koenker and Bassett [1].
  • ad hoc to paper A random 80:20 split yields a test set representative of future conditions.
    Section 3.5 justification for handling volatility; ignores temporal ordering and leaks future information into training.
  • domain assumption Sliding windows of length 6 preserve temporal dependencies.
    Section 3.3 uses overlapping windows; assumes this representation captures the dynamics needed for 5-step forecasts.
  • domain assumption Normalized RMSE values can be compared across studies with different normalization and splits.
    Section 5 compares RMSE 0.0112 to 0.0373 from Wu et al. [44] despite different split ratios and normalization.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantile deep learning models for multi-step ahead time series prediction." pith.science (2026). https://pith.science/paper/5ZTYW74G

@misc{pith2026241115674,
  author       = {Pith},
  title        = {Pith review of: Quantile deep learning models for multi-step ahead time series prediction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5ZTYW74G}},
  note         = {Machine review of arXiv:2411.15674}
}
read the original abstract

Uncertainty quantification is crucial in time series prediction, and quantile regression offers a valuable mechanism for uncertainty quantification which is useful for extreme value forecasting. Although deep learning models have been prominent in multi-step ahead prediction, the development and evaluation of quantile deep learning models have been limited. We present a novel quantile regression deep learning framework for multi-step time series prediction. In this way, we elevate the capabilities of deep learning models by incorporating quantile regression, thus providing a more nuanced understanding of predictive values. We provide an implementation of prominent deep learning models for multi-step ahead time series prediction and evaluate their performance under high volatility and extreme conditions. We include multivariate and univariate modelling, strategies and provide a comparison with conventional deep learning models from the literature. Our models are tested on two cryptocurrencies: Bitcoin and Ethereum, using daily close-price data and selected benchmark time series datasets. The results show that integrating a quantile loss function with deep learning provides additional predictions for selected quantiles without a loss in the prediction accuracy when compared to the literature. Our quantile model has the ability to handle volatility more effectively and provides additional information for decision-making and uncertainty quantification through the use of quantiles when compared to conventional deep learning models.

Figures

Figures reproduced from arXiv: 2411.15674 by the authors.

Figure 1
Figure 1. The uncertainty range provided in the demand forecast using quantile [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Bidirectional-LSTM network showing the flow of information. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Quantile recurrent neural network for one-step ahead and multi-step [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Framework diagram showing the key stages that include data processing model training and evaluation. We present quartile-based implementation for a [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Cryptocurrency time series reporting daily close prices [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Bitcoin time series: prediction plots of respective univariate and multivariate strategies (RMSE mean with 95% confidence interval given as error bar). [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Ethereum performance evaluation of respective Univariate and Multivariate deep learning models for 5 prediction horizons (mean RMSE with 95% [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: Performance evaluation of respective Univariate deep learning models, showing 10 step-ahead prediction horizons for benchmark datasets for 30 indepen [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Uncertainty-Aware Digital Twins: Robust Model Predictive Control using Time-Series Deep Quantile Learning

    eess.SY 2025-01 conditional novelty 5.0 of 10

    A robust MPC framework that uses one-shot multi-step TiDE predictions and learned quantile bounds as safety tubes, demonstrated on a DED additive-manufacturing simulator.

Reference graph

Works this paper leans on

102 extracted references · 65 canonical work pages · cited by 1 Pith paper

  1. [44]

    J. Wu, X. Zhang, F. Huang, H. Zhou, R. Chandra, Review of deep learn- ing models for crypto price prediction: implementation and evaluation, arXiv (2024). URL https://arxiv.org/abs/2405.11431

    work page Pith review arXiv 2024

  2. [1]

    Koenker, G

    R. Koenker, G. Bassett Jr, Regression quantiles, Econometrica: journal of the Econometric Society (1978) 33–50. URL https://www.jstor.org/stable/1913643

    arXiv 1978

  3. [2]

    Waldmann, Quantile regression: A short story on how and why, Sta- tistical Modelling 18 (3-4) (2018) 203–218

    E. Waldmann, Quantile regression: A short story on how and why, Sta- tistical Modelling 18 (3-4) (2018) 203–218. URL https://doi.org/10.1177/1471082X18759142

    work page doi:10.1177/1471082x18759142 2018

  4. [3]

    Y . Wei, R. D. Kehm, M. e. a. Goldberg, Applications for quantile regres- sion in epidemiology, Current Epidemiology Reports 6 (2019) 191–199

    2019

  5. [4]

    Fitzenberger, R

    B. Fitzenberger, R. Koenker, J. A. Machado, Economic applications of quantile regression, Springer Science & Business Media, 2013

    2013

  6. [5]

    B. e. a. Tillaguango, Impact of oil price, economic globalization, and in- flation on economic output: Evidence from latin american oil-producing countries using the quantile-on-quantile approach, Energy (2024). URL https://www.sciencedirect.com/science/article/ pii/S0360544224015597 1https://github.com/sydney-machine-learning/ quantiledeeplearning

    2024

  7. [6]

    Briollais, G

    L. Briollais, G. Durrieu, Application of quantile regression to recent ge- netic and-omic studies, Human genetics 133 (8) (2014) 951–966

    2014

  8. [7]

    D. E. Allen, P. Gerrans, R. e. a. Powell, Quantile regression: its applica- tion in investment analysis, Jassa 4 (2009) 7–12

    2009

Show all 102 references
  1. [8]

    Buchinsky, Changes in the us wage structure 1963-1987: Applica- tion of quantile regression, Econometrica: Journal of the Econometric Society (1994) 405–458

    M. Buchinsky, Changes in the us wage structure 1963-1987: Applica- tion of quantile regression, Econometrica: Journal of the Econometric Society (1994) 405–458

    1994

  2. [9]

    S. J. Sta ffa, D. S. Kohane, D. Zurakowski, Quantile regression and its applications: a primer for anesthesiologists, Anesthesia & Analgesia 128 (4) (2019) 820–830

    2019

  3. [10]

    G. S. Watson, Linear least squares regression, The Annals of Mathemat- ical Statistics (1967) 1679–1699

    1967

  4. [11]

    Geladi, B

    P. Geladi, B. R. Kowalski, Partial least-squares regression: a tutorial, Analytica chimica acta 185 (1986) 1–17

    1986

  5. [12]

    Vaysse, P

    K. Vaysse, P. Lagacherie, Using quantile regression forest to estimate uncertainty of digital soil mapping products, Geoderma 291 (2017) 55– 64

    2017

  6. [13]

    Dogulu, P

    N. Dogulu, P. L ´opez L ´opez, D. P. Solomatine, A. H. Weerts, D. L. Shrestha, Estimation of predictive hydrologic uncertainty using the quantile regression and uneec methods and their comparison on con- trasting catchments, Hydrology and Earth System Sciences 19 (7) (2015) 3181–3201

    2015

  7. [14]

    M. K. Ochi, On prediction of extreme values, Journal of Ship Research 17 (01) (1973) 29–37

    1973

  8. [15]

    R. P. Ribeiro, N. Moniz, Imbalanced regression and extreme value pre- diction, Machine Learning 109 (2020) 1803–1835

    2020

  9. [16]

    B. Wang, X. Zhou, Climate variation and prediction of rapid intensifica- tion in tropical cyclones in the western north pacific, Meteorology and Atmospheric Physics 99 (1) (2008) 1–16

    2008

  10. [17]

    Makkonen, Problems in the extreme value analysis, Structural safety 30 (5) (2008) 405–419

    L. Makkonen, Problems in the extreme value analysis, Structural safety 30 (5) (2008) 405–419

    2008

  11. [18]

    J. H. Lee, H. Kim, H. J. e. a. Park, Temporal prediction modeling for rainfall-induced shallow landslide hazards using extreme value distribu- tion, Landslides 18 (2021) 321–338

    2021

  12. [19]

    H. Xing, S. Junyi, H. Jin, The casualty prediction of earthquake disaster based on extreme learning machine method, Natural Hazards 102 (3) (2020) 873–886

    2020

  13. [20]

    X. Zhao, C. Scarrott, L. e. a. Oxley, Extreme value modelling for fore- casting market crisis impacts, Routledge, 2014

    2014

  14. [21]

    C. Wang, L. Zhang, G. Tao, Quantifying the influence of corrosion de- fects on the failure prediction of natural gas pipelines using generalized extreme value distribution (gevd) model and copula function with a case study, Emergency Management Science and Technology 4 (1) (2024)

    2024

  15. [22]

    Cumperayot, R

    P. Cumperayot, R. Kouwenberg, Early warning systems for currency crises: A multivariate extreme value approach, Journal of international money and finance 36 (2013) 151–171

    2013

  16. [23]

    T. B. Messervey, D. M. Frangopol, S. Casciati, Application of the statis- tics of extremes to the reliability assessment and performance prediction of monitored highway bridges, in: Structures and Infrastructure Sys- tems, Routledge, 2019, pp. 287–299

    2019

  17. [24]

    Y . Cai, D. Reeve, Extreme value prediction via a quantile function model, Coastal Engineering 77 (2013)

    2013

  18. [25]

    Velthoen, C

    J. Velthoen, C. Dombry, J. e. a. Cai, Gradient boosting for extreme quan- tile regression, Extremes 77 (2023) 639–667

    2023

  19. [26]

    B. Lim, S. Zohren, Time-series forecasting with deep learning: a survey, Philosophical Transactions of the Royal Society A 379 (2194) (2021) 20200209

    2021

  20. [27]

    J. F. Torres, D. Hadjout, A. Sebaa, F. Mart ´ınez- ´Alvarez, A. Troncoso, Deep learning for time series forecasting: a survey, Big Data 9 (1) (2021) 3–21

    2021

  21. [28]

    W. Fang, Q. Xue, L. e. a. Shen, Survey on the application of deep learn- ing in extreme weather prediction, Atmosphere 12 (6) (2021) 661

    2021

  22. [29]

    Z. Chen, H. Yu, Y . e. a. Geng, Evanet: An extreme value attention net- work for long-term air quality prediction, in: 2020 IEEE International Conference on Big Data (Big Data), IEEE, 2020, pp. 4545–4552

    2020

  23. [30]

    S. Gope, S. Sarkar, P. e. a. Mitra, Early prediction of extreme rainfall events: a deep learning approach, in: Advances in Data Mining. Ap- plications and Theoretical Aspects: 16th Industrial Conference, ICDM 2016, New York, NY , USA, July 13-17, 2016. Proceedings 16, Springer...

    2016

  24. [31]

    E. Chen, M. S. Andersen, R. Chandra, Deep learning framework with 16 bayesian data imputation for modelling and forecasting groundwater lev- els, Environmental Modelling & Software 178 (2024) 106072

    2024

  25. [32]

    G. e. a. Papacharalampous, Uncertainty estimation in spatial interpola- tion of satellite precipitation with ensemble learning, https://arxiv. org/abs/2403.10567 (2024)

    2024 arXiv

  26. [33]

    Tyralis, G

    H. Tyralis, G. Papacharalampous, A review of predictive uncertainty estimation with machine learning, Artificial Intelligence Review 57 (4) (2024) 94. URL https://link.springer.com/article/10.1007/ s10462-023-10698-8#Abs1

    2024

  27. [34]

    Y . Jia, J. H. Jeong, Deep learning for quantile regression under right censoring: Deepquantreg, Computational Statistics & Data Analysis 165 (2022) 107323

    2022

  28. [35]

    M. J. Van Strien, A. Gr ˆet-Regamey, A global time series of tra ffic volumes on extra-urban roads, Scientific data 11 (1) (2024) 470. URL https://www.nature.com/articles/ s41597-024-03287-z

    2024

  29. [36]

    S. Zhu, M. Zhang, C. e. a. Wang, A probabilistic runoff prediction model based on improved long short-term memory and interval correction, Journal of Hydrologic Engineering 29 (4) (2024) 04024018

    2024

  30. [37]

    J. Hu, J. Tang, Z. Liu, A novel time series probabilistic prediction approach based on the monotone quantile regression neural network, Information Sciences 654 (2024) 119844. URL https://www.sciencedirect.com/science/article/ pii/S0020025523014299

    2024

  31. [38]

    Zhang, H

    W. Zhang, H. Quan, D. Srinivasan, An improved quantile regression neural network for probabilistic load forecasting, IEEE Transactions on Smart Grid 10 (4) (2018) 4425–4434

    2018

  32. [39]

    J. Hu, J. Tang, Z. Liu, A novel time series probabilistic prediction ap- proach based on the monotone quantile regression neural network, In- formation Sciences 119844 (2023)

    2023

  33. [40]

    Tang, et al., Neural networks for partially linear quantile regression, Journal of Business & Economic Statistics (2023)

    J. Tang, et al., Neural networks for partially linear quantile regression, Journal of Business & Economic Statistics (2023). URL https://www.tandfonline.com/doi/abs/10.1080/ 07350015.2023.2208183

    2023

  34. [41]

    M. et al., A conceptual model of investment-risk prediction in the stock market using extreme value theory with machine learning: a semisys- tematic literature review, Risks 11 (3) (2023) 60. URL https://www.mdpi.com/2227-9091/11/3/60

    2023

  35. [42]

    A.-A. e. a. Ibn Musah, The asymptotic decision scenarios of an emerg- ing stock exchange market: Extreme value theory and artificial neural network, Risks 6 (4) (2018) 132. URL https://www.mdpi.com/2227-9091/6/4/132

    2018

  36. [43]

    M. e. a. Melina, Modeling of machine learning-based extreme value theory in stock investment risk prediction: A systematic literature review, Big Data (2024). URL https://www.liebertpub.com/doi/abs/10.1089/big. 2023.0004

    2024

  37. [45]

    Hochreiter, J

    S. Hochreiter, J. Schmidhuber, Long short-term memory, Neural com- putation 9 (8) (1997) 1735–1780

    1997

  38. [46]

    Alzubaidi, J

    L. Alzubaidi, J. Zhang, A. J. Humaidi, et al., Review of deep learning: concepts, cnn architectures, challenges, applications, future directions, Journal of Big Data 8 (2021) 1–74

    2021

  39. [47]

    Chandra, S

    R. Chandra, S. Goyal, R. Gupta, Evaluation of deep learning models for multi-step ahead time series prediction, IEEE Access 9 (2021) 83105– 83123

    2021

  40. [48]

    H. Zhu, H. Xia, Y . Guo, C. Peng, The heterogeneous e ffects of urban- ization and income inequality on co2 emissions in brics economies: ev- idence from panel quantile regression, Environmental Science and Pol- lution Research 25 (2018) 17176–17193

    2018

  41. [49]

    Koenker, Quantile regression for longitudinal data, Journal of multi- variate analysis 91 (1) (2004) 74–89

    R. Koenker, Quantile regression for longitudinal data, Journal of multi- variate analysis 91 (1) (2004) 74–89

    2004

  42. [50]

    Cai, Regression quantiles for time series, Econometric theory 18 (1) (2002) 169–192

    Z. Cai, Regression quantiles for time series, Econometric theory 18 (1) (2002) 169–192. URL https://www.cambridge.org/core/ journals/econometric-theory/article/abs/ regression-quantiles-for-time-series/ 485A99DE06615C32AA41D737D8E29A77

    2002

  43. [51]

    Xiao, Time series quantile regressions, in: Handbook of statistics, V ol

    Z. Xiao, Time series quantile regressions, in: Handbook of statistics, V ol. 30, Elsevier, 2012, pp. 213–257. URL https://www.sciencedirect.com/science/article/ abs/pii/B9780444538581000090

    2012

  44. [52]

    Koenker, Quantile regression: 40 years on, Annual review of economics 9 (2017) 155–176

    R. Koenker, Quantile regression: 40 years on, Annual review of economics 9 (2017) 155–176. URL https://www.annualreviews.org/content/journals/ 10.1146/annurev-economics-063016-103651#right-ref-B44

    2017 doi

  45. [53]

    A. J. McNeil, Extreme value theory for risk managers, Departement Mathematik ETH Zentrum 12 (5) (1999) 217–237

    1999

  46. [54]

    Pickands III, Statistical inference using extreme order statistics, The Annals of Statistics (1975) 119–131

    J. Pickands III, Statistical inference using extreme order statistics, The Annals of Statistics (1975) 119–131

    1975

  47. [55]

    T. G. Bali, The generalized extreme value distribution, Economics letters 79 (3) (2003) 423–427

    2003

  48. [56]

    Castillo, A

    E. Castillo, A. S. Hadi, Fitting the generalized Pareto distribution to data, Journal of the American Statistical Association 92 (440) (1997) 1609– 1620

    1997

  49. [57]

    Ferreira, L

    A. Ferreira, L. De Haan, On the block maxima method in extreme value theory: Pwm estimators, The Annals of statistics (2015) 276–298. URL http://www.jstor.org/stable/43556515

    2015

  50. [58]

    Fr ´echet, Sur la loi de probabilit´e de l’´ecart maximum, Ann

    M. Fr ´echet, Sur la loi de probabilit´e de l’´ecart maximum, Ann. de la Soc. Polonaise de Math. (1927)

    1927

  51. [59]

    R. A. Fisher, L. H. C. Tippett, Limiting forms of the frequency distribu- tion of the largest and smallest member of a sample, Proc. Cambridge Philosophical Society 24 (1928) 180–190

    1928

  52. [60]

    V . F. Pisarenko, A. Sornette, D. Sornette, et al., Characterization of the tail of the distribution of earthquake magnitudes by combining the gev and gpd descriptions of extreme value theory, Pure and Applied Geo- physics 171 (2014) 1599–1624

    2014

  53. [61]

    B ¨ucher, C

    A. B ¨ucher, C. Zhou, A horse race between the block maxima method and the peak–over–threshold approach, Statistical Science 36 (3) (2021) 360–378. URL https://projecteuclid.org/journals/ statistical-science/volume-36/issue-3/ A-Horse-Race-between-the-Block-Maxima-Method-and-t...

    2021 doi

  54. [62]

    T. H. Soukissian, C. Tsalis, The e ffect of the generalized extreme value distribution parameter estimation methods in extreme wind speed pre- diction, Natural Hazards 78 (2015) 1777–1809

    2015

  55. [63]

    J. Schaumburg, Predicting extreme value at risk: Nonparametric quantile regression with refinements from extreme value theory, Computational Statistics & Data Analysis 56 (12) (2012) 4081–4096

    2012

  56. [64]

    F. F. do Nascimento, D. Gamerman, H. F. Lopes, A semiparametric bayesian approach to extreme value estimation, Statistics and Comput- ing 22 (2012) 661–675

    2012

  57. [65]

    H. B. Sandya, P. H. Kumar, S. B. Patil, Feature extraction, classification and forecasting of time series signal using fuzzy and garch techniques, in: Proceedings of the National Conference on Challenges in Research and Technology in the Coming Decades (CRT), 2013, pp. 1–7

    2013

  58. [66]

    L. C. Chang, P. A. Chen, F. J. Chang, Reinforced two-step-ahead weight adjustment technique for online training of recurrent neural networks, IEEE Transactions on Neural Networks and Learning Systems 23 (8) (2012) 1269–1278. doi:10.1109/TNNLS.2012.2200695

    2012

  59. [67]

    R. W. V . S. Khedkar, R. Chandra, Evaluation of deep learning models for australian climate extremes: prediction of streamflow and floods (2024). arXiv:2407.15882. URL https://arxiv.org/abs/2407.15882

    2024 arXiv

  60. [68]

    Lampinen, A

    J. Lampinen, A. Vehtari, Bayesian approach for neural net- works—review and case studies, Neural Networks 14 (3) (2001) 257– 274

    2001

  61. [69]

    Kononenko, Bayesian neural networks, Biological Cybernetics 61 (5) (1989) 361–370

    I. Kononenko, Bayesian neural networks, Biological Cybernetics 61 (5) (1989) 361–370

    1989

  62. [70]

    H. Jang, J. Lee, An empirical study on modeling and prediction of bit- coin prices with bayesian neural networks based on blockchain informa- tion, IEEE Access 6 (2017) 5427–5437

    2017

  63. [71]

    Chandra, Y

    R. Chandra, Y . He, Bayesian neural networks for stock price forecast- ing before and during covid-19 pandemic, PLoS ONE 16 (7) (2021) e0253217. doi:10.1371/journal.pone.0253217

    2021 doi

  64. [72]

    A. G. Wang, Y ., B. Martin-Barragan, Machine learning approaches to forecasting cryptocurrency volatility: Considering internal and exter- 17 nal determinants, International Review of Financial Analysis 90 (2023) 102914

    2023

  65. [73]

    Van Houdt, C

    G. Van Houdt, C. Mosquera, G. N ´apoles, A review on the long short- term memory model, Artificial Intelligence Review 53 (12 2020). doi: 10.1007/s10462-020-09838-1

    2020 doi

  66. [74]

    J. L. Elman, Finding structure in time, Cognitive Science 14 (2) (1990) 179–211

    1990

  67. [75]

    S. Hochreiter, The vanishing gradient problem during learning recurrent neural nets and problem solutions, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 6 (02) (1998) 107–116

    1998

  68. [76]

    Graves, J

    A. Graves, J. Schmidhuber, Framewise phoneme classification with bidi- rectional lstm and other neural network architectures, Neural Networks 18 (5-6) (2005) 602–610

    2005

  69. [77]

    Y . Yu, X. Si, C. Hu, J. Zhang, A review of recurrent neural net- works: LSTM cells and network architectures, Neural computation 31 (7) (2019) 1235–1270

    2019

  70. [78]

    Sutskever, O

    I. Sutskever, O. Vinyals, Q. V . Le, Sequence to sequence learning with neural networks, in: Advances in Neural Information Processing Sys- tems, V ol. 27, 2014

    2014

  71. [79]

    X. Shi, Z. Chen, H. Wang, D.-Y . Yeung, W.-K. Wong, W.-c. Woo, Con- volutional lstm network: A machine learning approach for precipitation nowcasting, in: Advances in Neural Information Processing Systems, V ol. 28, 2015

    2015

  72. [80]

    Hecht-Nielsen, Theory of the backpropagation neural network, in: Neural Networks for Perception, Academic Press, 1992, pp

    R. Hecht-Nielsen, Theory of the backpropagation neural network, in: Neural Networks for Perception, Academic Press, 1992, pp. 65–93

    1992

  73. [81]

    Hinaut, N

    X. Hinaut, N. Trouvain, Mackey-glass timeseries dataset, https://reservoirpy.readthedocs.io/en/latest/api/ generated/reservoirpy.datasets.mackey_glass.html (2021)

    2021

  74. [82]

    M. C. Mackey, L. Glass, Oscillation and chaos in physiological con- trol systems, Science 197 (4300) (1977) 287–289. doi:10.1126/ science.267326

    1977

  75. [83]

    E. N. Lorenz, The statistical prediction of solutions of dynamic equations, Proceedings of the International Symposium on Numerical Weather Prediction (1960) 628–635. URL https://web.archive.org/web/20190523190103/http: //eaps4.mit.edu/research/Lorenz/The_Statistical_ Predicti...

    1960

  76. [84]

    D. P. Kingma, J. Ba, Adam: A method for stochastic optimization (2017). arXiv:1412.6980. URL https://arxiv.org/abs/1412.6980

    2017 arXiv

  77. [85]

    Greaves, B

    A. Greaves, B. Au, Using the bitcoin transaction graph to predict the price of bitcoin, 2015. URL https://api.semanticscholar.org/CorpusID:18038866

    2015

  78. [86]

    R. Y . Chou, Forecasting financial volatilities with extreme values: the conditional autoregressive range (carr) model, Journal of Money, Credit and Banking (2005) 561–582

    2005

  79. [87]

    X. Zhao, C. Scarrott, L. Oxley, M. Reale, Extreme value modelling for forecasting market crisis impacts, in: The Global Financial Crisis, Rout- ledge, 2014, pp. 61–70

    2014

  80. [88]

    W. J. Dixon, Analysis of extreme values, The Annals of Mathematical Statistics 21 (4) (1950) 488–506

    1950

  81. [89]

    B. Merz, A. H. Thieken, Flood risk curves and uncertainty bounds, Nat- ural Hazards 51 (2009) 437–458

    2009

  82. [90]

    L. Yang, A. Shami, On hyperparameter optimization of machine learn- ing algorithms: Theory and practice, Neurocomputing 415 (2020) 295– 316

    2020

  83. [91]

    Muthukrishnan, R

    R. Muthukrishnan, R. Rohini, Lasso: A feature selection technique in predictive modeling for machine learning, in: 2016 IEEE International Conference on Advances in Computer Applications (ICACA), IEEE, 2016, pp. 18–20

    2016

  84. [92]

    W. N. van Wieringen, Lecture notes on ridge regression, arXiv preprint arXiv:1509.09169 (Sep 2015)

    2015 arXiv

  85. [93]

    Wager, S

    S. Wager, S. Wang, P. S. Liang, Dropout training as adaptive regulariza- tion, Advances in Neural Information Processing Systems 26 (2013)

    2013

  86. [94]

    I. S. Al-Tameemi, M. R. Feizi-Derakhshi, S. Pashazadeh, M. Asadpour, Multi-model fusion framework using deep learning for visual-textual sentiment classification, Computers, Materials & Continua 76 (2) (2023) 2145–2177

    2023

  87. [95]

    Zhang, Y

    W. Zhang, Y . Deng, B. Liu, S. J. Pan, L. Bing, Sentiment analysis in the era of large language models: A reality check, arXiv preprint arXiv:2305.15005 (May 2023)

    2023 arXiv

  88. [96]

    R. M. Neal, Bayesian Learning for Neural Networks, V ol. 118, Springer New York, 1996

    1996

  89. [97]

    Y . Yoon, G. J. S, T. M. Margavio, A comparison of discriminant analysis versus artificial neural networks, Journal of the Operational Research Society 44 (1) (1993) 51–60. doi:10.1057/jors.1993.6

    1993 doi

  90. [98]

    D. J. C. MacKay, A practical bayesian framework for backpropagation networks, Neural Computation 4 (3) (1992) 448–472. doi:10.1162/ neco.1992.4.3.448

    1992

  91. [99]

    Zhang, C

    R. Zhang, C. Li, J. Zhang, C. Chen, A. G. Wilson, Cyclical stochastic gradient mcmc for bayesian deep learning, arXiv preprint arXiv:1902.03932 (Feb 2019)

    1902 arXiv

  92. [100]

    Attias, Inferring parameters and structure of latent variable models by variational bayes, arXiv preprint arXiv:1301.6676 (Jan 2013)

    H. Attias, Inferring parameters and structure of latent variable models by variational bayes, arXiv preprint arXiv:1301.6676 (Jan 2013)

    2013 arXiv

  93. [101]

    Chaput, J

    B. Chaput, J. C. Girard, M. Henry, Frequentist approach: Modelling and simulation in statistics and probability teaching, in: Teaching Statistics in School Mathematics—Challenges for Teaching and Teacher Educa- tion: A Joint ICMI/IASE Study: The 18th ICMI Study, 2011, pp. 85–95

    2011

  94. [102]

    Afrifa-Yamoah, U

    E. Afrifa-Yamoah, U. A. Mueller, S. M. Taylor, A. J. Fisher, Missing data imputation of high-resolution temporal climate time series data, Meteorological Applications 27 (1) (2020) e1873. Appendix A. Prediction quantiles 18 (a) Univariate Quantile BD-LSTM (b) Multivariate Quan...

    2020

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.