Quantile Convolutional Neural Networks for Value at Risk Forecasting

G\'abor Petneh\'azi

REVIEW 4 major objections 6 minor 21 references

Quantile Convolutional Neural Networks for Value at Risk Forecasting

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A convolutional network trained jointly on many stocks' histories can forecast Value at Risk with exceedance rates close to nominal levels, beating constant, GARCH, and linear quantile regression baselines.

desk verdict Joint multi-asset training helps quantile CNNs for VaR, but the evidence is thinner than the conclusion. read the letter →

arxiv 1908.07978 v4 pith:OQ7NOG4R submitted 2019-08-21 cs.LG q-fin.CPstat.ML

Gábor Petneházi This is my paper · ORCID

classification cs.LGq-fin.CPstat.ML

keywords ValueatRiskquantileregressionconvolutionalneuralnetworkdilatedcausalconvolutiontimeseriesforecastingmulti-assetlearningDynamictesttail

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 proposes a one-dimensional convolutional neural network that forecasts quantiles of daily stock returns directly, rather than forecasting the mean. The network is trained with a quantile (pinball) loss, so its output is an estimate of a Value at Risk level such as the 1% or 5% tail quantile. The central claim is that when the network is trained jointly on the price histories of many stocks, it produces one-day-ahead VaR forecasts with exceedance rates close to the nominal levels and with fewer Dynamic Quantile test rejections than constant, GARCH(1,1), and linear quantile regression baselines. If true, this means that pooling extreme events across assets can make deep quantile forecasting work despite the scarcity of tail data for any single stock, and that the resulting risk budgets are cheaper than those from a historical constant estimate.

What carries the argument

Three components carry the argument. (1) The pinball quantile loss replaces mean squared error so that the network's output is a conditional quantile, i.e., a VaR estimate, without distributional assumptions. (2) The network is a WaveNet-style stack of six causal convolutional layers with eight filters of kernel size 2, ReLU activations, and exponentially increasing dilation rates ($2^{l-1}$), followed by a $1\times 1$ convolution with a linear activation; causal dilated convolutions give an exponential receptive field so the 128-step input window can predict one step ahead. (3) Joint training feeds the overlapping 128-return windows from all 100 stocks into the same network, so the model learns from pooled tail events rather than from a single asset's history. The claim is that these three pieces together produce calibrated one-day-ahead VaR forecasts at 95%, 99%, and 99.9% confidence.

What would settle it

Train the joint QCNN on 100 stocks and evaluate it on a held-out set of stocks from a market or sector that was deliberately absent from training, for example train on US equities and test on European equities. The central claim predicts that exceedance rates stay near nominal and the Dynamic Quantile rejection rate stays low; if instead the rejection rate rises to the level of the single-stock QCNN, the pooling benefit depends on shared tail sources and does not generalize.

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Extended reading notes

Core claim

The discovery is that quantile forecasting with a convolutional neural network works for Value at Risk when the network is trained jointly on multiple assets, and fails when trained on a single asset's history alone. The QCNN is a causal, dilated, one-dimensional convolutional network whose final layer outputs a $\theta$-quantile of the next day's return, optimized with the asymmetric absolute loss $\theta\sum_{y_i \ge \hat q_i}(y_i-\hat q_i) + (\theta-1)\sum_{y_i < \hat q_i}(y_i-\hat q_i)$. In the empirical study on 100 US-listed stocks, the single-stock QCNN overshoots the targeted exceedance rates by up to an order of magnitude, while the joint QCNN trained on all 100 stocks gives mean exceedance rates of 0.0433, 0.0115, and 0.0023 for the 95%, 99%, and 99.9% levels—close to the nominal 0.05, 0.01, and 0.001—and has lower average DQ-test rejection rates (0.05 and 0.16 at the 5% and 1% significance levels for 95% VaR) than all baselines, with lower average VaR values than the constant historical estimate.

Load-bearing premise

The load-bearing premise is that the daily returns of different stocks have similar enough tail behavior—common sources of extreme events—that one network trained on many assets can learn valid quantiles for any single asset; if tails are idiosyncratic, the joint model's calibration could be an artifact of pooling rather than a real transferable property.

Editorial extensions

If this is right

If the central claim is correct, VaR can be produced nonparametrically: no normality or t-distribution assumption is needed, because the network learns the empirical tail directly from returns.
Joint training is the load-bearing ingredient for deep quantile models: with only one stock's history the same architecture grossly overshoots exceedance rates, so pooling many assets is what makes the data volume sufficient.
Better calibration transfers into capital: the joint QCNN's average VaR values are lower than the constant historical estimate's while maintaining similar exceedance rates, meaning a bank or portfolio using it would set aside less capital for the same coverage.
The low Dynamic Quantile rejection rates indicate that the joint model's exceedances are not only correctly frequent but also correctly timed—past exceedances and VaR levels have little explanatory power for future hits.

Reading between the lines

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

A natural next test the paper does not run: train the joint QCNN on stocks from one sector or market and test on a held-out sector or market; if the calibration holds, the transfer is general, and if it degrades, the benefit depends on the training and test stocks sharing tail sources.
The paper's explanation for pooling—'more stocks have experienced more extreme events, and we may expect them to have similar sources'—suggests a data-economy interpretation: the effective sample size for tail estimation is the number of pooled extreme events, not the length of any one series. That interpretation could be tested by varying the number of training assets and observing whether DQ rej
The same pinball-loss architecture should apply to expected shortfall by swapping the loss for a coherent tail-loss function, and to intraday or high-frequency returns, though neither is evaluated here.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take on Petneházi's QCNN paper. The genuinely new thing is the joint multi-asset training of a quantile CNN for VaR; the architecture itself is a known WaveNet-style dilated causal CNN with a pinball loss. The paper reports a real empirical result: a QCNN trained on 100 stocks at once gives better-calibrated one-day-ahead VaR exceedance rates and lower Dynamic Quantile rejection rates than constant, GARCH, and linear QR baselines, at lower average VaR. That is practically useful if it holds. Credit is due for honest reporting: the single-stock QCNN fails badly (95% exceedance rate 12.7% vs nominal 5%), and the paper says so rather than hiding it. The repeated experiment on 1999-2008 data is also a nice check.

Soft spots are real but mostly about evidence quality, not fatal logic. There is no code or data release, no significance tests or confidence intervals on the differences between methods, and no sensitivity analysis around the chosen architecture (6 layers, 8 filters, kernel size 2, 128-step window). The paper cites LSTM quantile regression and QARNN in the introduction but does not compare against them—that is a missed baseline that matters for an empirical claim. The stress-test worry about 'similar sources' is somewhat overplayed: even if joint training works simply because 100 stocks give the network a hundred times more tail events, that is not an artifact; it is the mechanism. But the homogeneity assumption is untested, and the paper gives no split-sample or synthetic experiment varying tail heterogeneity, so we do not know whether the result transfers to a different stock universe. That is a legitimate limitation, not a load-bearing flaw.

For the right reader—an applied quant researcher or risk manager interested in simple deep learning tools for VaR—this is worth reading. It deserves a serious referee: the central claim is clear, falsifiable, and the method is simple enough to reproduce if code appears. I would send it to peer review with a request for code, significance testing, sensitivity analysis, and a direct comparison with a quantile LSTM. My own verdict is conditional, but the condition is standard empirical rigor, not a novel problem.

Referee Report

4 major / 6 minor

Summary. This paper proposes a quantile convolutional neural network (QCNN), a one-dimensional dilated causal CNN trained with the pinball loss, for one-day-ahead Value at Risk forecasting. The model is evaluated on daily log returns of 100 randomly selected US stocks over 2009-2018, with the last 30% as test set. The authors compare a per-stock QCNN and a joint QCNN trained on all stocks against a constant quantile estimator, a normal GARCH(1,1), and a linear quantile autoregression. The reported tables show that the joint QCNN yields exceedance rates closer to the nominal 95%, 99%, and 99.9% levels, lower standard deviations of exceedance rates, and lower Dynamic Quantile test rejection rates than all baselines, while the single-stock QCNN is badly miscalibrated. The paper concludes that training on multiple assets improves VaR forecasts.

Significance. The central empirical claim—that the joint QCNN improves quantile calibration relative to standard baselines—is plausible and, if confirmed, practically useful: VaR forecasts that are both accurately calibrated and less conservative than a historical quantile are valuable for risk budgeting. The authors are to be credited for evaluating out-of-sample with a standard backtesting test, for reporting exceedance rates, and for including simple baselines rather than only neural alternatives. However, the statistical support is incomplete: no significance tests, no confidence intervals, and no control experiment separate the effect of larger sample size from the claimed cross-asset tail pooling. The paper is clearly written and the QCNN idea is presented transparently, but the empirical evidence as reported is not yet at the standard needed to support the strong conclusions in Section 3.5.

major comments (4)

[Section 3.5, Tables 1–3] The comparisons are based solely on point estimates (means, medians, standard deviations) with no significance tests or confidence intervals. Because the same 100 stocks are used for every method, paired tests are available; for example, a paired sign test or bootstrap on the per-stock exceedance-rate difference between Joint QCNN and GARCH would directly assess whether the reported gap (0.0433 vs. 0.0347 at the 95% level) is systematic. Likewise, the DQ rejection rates are proportions out of 100 stocks, so binomial confidence intervals should accompany them. Without such measures, the claim in the text that the joint QCNN 'produces the highest quality VaR estimates' is not statistically established.
[Section 3.1 and Section 3.5] The rationale for joint training is that extreme returns across different stocks 'may ... have similar sources,' but this assumption is never tested, and the reported comparison of Joint QCNN with single-stock QCNN conflates cross-asset pooling with a roughly 100-fold increase in training data. The authors should add a control that holds sample size fixed while destroying the cross-asset structure, such as training the same architecture on a random permutation of the returns across the 100 stocks, or on the pooled returns with the asset index removed. If the permuted/pooled model matches Joint QCNN's performance, the improvement is attributable to sample size rather than to shared tail dynamics; otherwise the stated 'similar sources' mechanism receives support. This distinction is load-bearing for the paper's contribution, which is explicitly about learning from multiple assets.
[Section 3.4, Eq. (6) and Tables 1–2] Assigning a p-value of 0 to zero-exceedance forecasts is not part of the Engle-Manganelli Dynamic Quantile test as defined by Eq. (6). When Hit has no variation, the regression in Eq. (5) is degenerate and the chi-square approximation is invalid, so a pre-specified replacement rule can bias the reported rejection rates. The authors should report the frequency of zero-exceedance forecasts for each method, justify the 0-p-value rule, and show that the DQ rejection-rate comparisons are robust to an alternative treatment (e.g., excluding such stocks or using an exact test).
[Section 3.3] The joint QCNN training and evaluation protocol is underspecified. It is not stated whether the standardization ('subtracting the mean and dividing by the standard deviation') is computed per asset or globally, how training minibatches are composed from the 100 stocks, or whether the single trained network is applied to each stock's test sequence without any asset-specific conditioning. These details determine whether the network can in principle learn asset-specific tail behavior, and they are necessary for reproducing Tables 1–3. Please spell out the protocol and, if relevant, provide code.

minor comments (6)

[Section 1] The phrase 'slided local receptive fields' should be 'sliding local receptive fields'; there are also typographical spacing errors such as 'V aR' in the abstract.
[Section 2.2, Eq. (1)] The quantile loss is written with summation subscripts that are hard to parse; use the standard pinball loss ρ_θ(u)=u(θ−1{u<0}) and sum over the batch.
[Section 3.3] The statement 'The output sequences are the inputs shifted by 1 step' should clarify how the target value for the one-day-ahead VaR forecast is extracted from the output sequence.
[Section 3.5] The robustness statement that 'the results were quite similar' for 1999–2008 is not accompanied by any numbers; include the corresponding table or remove the claim.
[Section 3.4] State explicitly why DQ test results are not reported for the 99.9% level; presumably the expected number of exceedances is too small for the asymptotic test.
[General] No code or data-publication link is provided; for an empirical study of this kind, releasing the implementation would substantially increase confidence in the results.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the QCNN is trained with the quantile loss and evaluated out-of-sample with the Dynamic Quantile test, with no parameter fitted to the test outcome.

full rationale

The paper's claim is empirical, not derivational. The QCNN is trained by minimizing the check loss (Eq. 1) on training returns, and then evaluated one-day-ahead on the last 30% of each series, where Tables 1 to 3 report exceedance rates and Dynamic Quantile test rejection rates. Nothing in the paper fits any constant to the test-set exceedance rates or DQ results; the network weights are optimized to the quantile objective, and the DQ test is an external misspecification test based on the Hit variable (Eqs. 4 to 6). The joint QCNN is a modeling choice motivated, not derived, by the statement that stocks 'have experienced more extreme events, and we may expect them to have similar sources'; even if this tail-homogeneity assumption were false, that would be an empirical robustness concern, not circularity. The paper contains no self-citation chain: all cited methods are external prior work (e.g., CAViaR, WaveNet), and no cited result is equivalent to the paper's conclusion. Thus no claimed prediction reduces to its input by construction.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The model's trainable weights are estimated by minimizing the quantile loss, which is standard estimation rather than an ad hoc free parameter. The key ad hoc choices are the architecture hyperparameters, which are picked by hand without sensitivity analysis. The central scientific assumption of cross-asset tail similarity is borrowed without independent validation beyond this one experiment. No new physical entities are introduced.

free parameters (1)

Architecture hyperparameters
Number of layers (6), filters per layer (8), kernel size (2), dilation schedule 2^(l-1), input length (128), training epochs (128), batch size (128), and adadelta optimizer are selected by hand without a reported search. The performance of the joint QCNN depends on these choices, and no sensitivity analysis is provided.

assumptions (5)

standard math Minimizing the quantile loss in Eq. (1) yields the conditional quantile of the target distribution.
This is the standard justification for quantile regression, cited via Koenker and Hallock (2001). The paper relies on it to connect the network output to VaR.
standard math The Dynamic Quantile test statistic in Eq. (6) is asymptotically chi-square distributed.
The paper uses the DQ test to validate model calibration. This rests on standard asymptotic theory for regression-based specification tests.
domain assumption Daily stock returns across different assets share common tail dynamics that can be learned jointly.
Section 3.1 states that more stocks provide more extreme events and that similar sources are expected. The joint QCNN result depends on this transferability assumption.
domain assumption The Kaggle stock dataset accurately represents U.S. stock return behavior for the studied periods.
All empirical conclusions rely on the dataset's correctness and representativeness. The paper does not validate the data or the random stock selection beyond a single repeat period.
domain assumption The fixed hyperparameters are adequate without tuning.
The paper reports no hyperparameter search and no seed averaging. The reported results are a single run of a chosen architecture, so the conclusion assumes this run is representative.

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Cite this review

Pith. "Pith review of Quantile Convolutional Neural Networks for Value at Risk Forecasting." pith.science (2026). https://pith.science/paper/OQ7NOG4R

@misc{pith2026190807978,
  author       = {Pith},
  title        = {Pith review of: Quantile Convolutional Neural Networks for Value at Risk Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OQ7NOG4R}},
  note         = {Machine review of arXiv:1908.07978}
}

read the original abstract

This article presents a new method for forecasting Value at Risk. Convolutional neural networks can do time series forecasting, since they can learn local patterns in time. A simple modification enables them to forecast not the mean, but arbitrary quantiles of the distribution, and thus allows them to be applied to VaR-forecasting. The proposed model can learn from the price history of different assets, and it seems to produce fairly accurate forecasts.

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

An empirical evaluation of generic convolutional and recurrent networks for sequence modeling

Shaojie Bai, J Zico Kolter, and Vladlen Koltun. An empirical evaluation of generic convolutional and recurrent networks for sequence modeling. arXiv preprint arXiv:1803.01271, 2018

arXiv 2018

[2] [2]

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Anastasia Borovykh, Sander Bohte, and Cornelis W Oosterlee. Conditional time series forecasting with convolutional neural networks. arXiv preprint arXiv:1703.04691, 2017

arXiv 2017

[3] [3]

Application of quantile regression to estimation of value at risk

Mei-Yuan Chen and Jau-Er Chen. Application of quantile regression to estimation of value at risk. Review of Financial Risk Management, 1 0 (2): 0 15, 2002

work page 2002

[4] [4]

Garch 101: The use of arch/garch models in applied econometrics

Robert Engle. Garch 101: The use of arch/garch models in applied econometrics. Journal of economic perspectives, 15 0 (4): 0 157--168, 2001

work page 2001

[5] [5]

Caviar: conditional value at risk by quantile regression

Robert F Engle and Simone Manganelli. Caviar: conditional value at risk by quantile regression. Technical report, National Bureau of Economic Research, 1999

work page 1999

[6] [6]

Portfolio value-at-risk with heavy-tailed risk factors

Paul Glasserman, Philip Heidelberger, and Perwez Shahabuddin. Portfolio value-at-risk with heavy-tailed risk factors. Mathematical Finance, 12 0 (3): 0 239--269, 2002

work page 2002

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work page 1998

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Philippe Jorion. Value at risk. 2000

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