peltwtcn

A faithful Python implementation of the PELT → wavelet → deep-learning carbon price forecasting framework, with the replication audit the paper needs.

Implements

Ren, R., Li, J., Li, Y., Huang, S., Shen, J., Li, W., Le, J. and Wang, S. (2025) "A Hybrid Deep Learning based Carbon Price Forecasting Framework with Structural Breakpoints Detection and Signal Denoising", arXiv:2511.04988.

Author of this package: Dr Merwan Roudane — merwanroudane920@gmail.com — github.com/merwanroudane

Everything is built on the real EU ETS dataset — 6,113 daily EUA observations from 2007-09-10 to 2024-06-04, matching the paper exactly. Nothing here is simulated.

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Table of contents

1. What this package does
2. Installation
3. Sixty-second quick start
4. The three protocols
5. Results
6. What the replication found
7. The real dataset
8. Module map
9. Documentation
10. Testing
11. Citation
12. Author

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1. What this package does

The paper's pipeline, end to end, in one call — plus the diagnostics it omits.

• Three structural break detectors — PELT (Killick et al., 2012), ICSS (Inclán & Tiao, 1994), Bai–Perron (2003), and the combined BP&ICSS baseline of Lin & Zhang (2022).
• Wavelet denoising in the paper's two-sided form and a leakage-free rolling form.
• LSTM, GRU and TCN in Keras, with the paper's exact hyper-parameters. The TCN's dilated causal convolution is written from scratch so it runs on a CPU and is verified for strict causality.
• Live data loaders for the EUA price and its drivers, with a bundled cache.
• Publication-quality tables and figures — LaTeX/booktabs, Markdown, HTML, CSV, Excel; every figure of the paper at 300 dpi.
• Diebold–Mariano and Model Confidence Set tests, plus a random-walk benchmark and Theil's U. The paper reports none of these.
• The published Table 1 as a checkable constant, so any run can be diffed against it.

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2. Installation

git clone https://github.com/merwanroudane/peltwtcn.git
cd peltwtcn
pip install -e ".[all]"

Extras: [deep] TensorFlow · [data] yfinance + openpyxl · [plots] seaborn · [test] pytest. Without TensorFlow everything except the three networks still works.

Requires Python ≥ 3.9.

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3. Sixty-second quick start

import peltwtcn as pw

# 1. the real EUA carbon price plus 13 exogenous drivers
df = pw.load_paper_dataset()
print(df.shape)                      # (6113, 14)

# 2. the paper's best model, in a configuration that works out of sample
pipe = pw.PELTWTPipeline(model="tcn", stationary=True).fit(df)
print(pipe.summary())

# 3. all five specifications of Table 1
res = pw.run_experiment(df, stationary=True)
print(pw.results_table(res.table, fmt="markdown"))

# 4. how does it compare with the published numbers?
print(pw.compare_with_paper(res.table))

# 5. every figure, at 300 dpi
pw.set_journal_style()
pw.save_all_figures(res, df, outdir="assets")

The full replication, all three protocols, tables and figures:

python examples/run_full_replication.py

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4. The three protocols

The paper's specification does not survive an honest chronological split. Rather than quietly fix it, this package implements all three variants and reports them side by side.

Protocol	Call	What it is
A level	mode="paper", stationary=False	The faithful replication — the paper's specification, literally. Does not work out of sample.
B stationary	mode="paper", stationary=True	Same models, same hyper-parameters, applied to the first difference. Levels rebuilt as last value + predicted change, so metrics stay in EUR.
C causal	mode="causal", stationary=True	Adds a causal wavelet, a training-only scaler and a raw target. The only protocol whose numbers are an honest out-of-sample claim.

mode="causal" forces the leak-free settings, so you cannot leave one in by accident.

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5. Results

Protocol B on the real dataset, the paper's own settings (50 epochs, early stopping), sorted by RMSE:

Model	MAE	RMSE	MAPE (%)	R²	Theil U	Train (s)
Random walk	0.8457	1.2230	1.1571	0.9934	1.0000	0.0
PELT-WT-GRU	0.8484	1.2361	1.1611	0.9933	1.0107	79.1
PELT-WT-LSTM (multi)	0.8930	1.2615	1.2292	0.9930	1.0315	64.9
BP&ICSS-WT-LSTM	0.9210	1.2847	1.2583	0.9928	1.0505	76.7
PELT-WT-LSTM (uni)	1.0078	1.3459	1.4313	0.9920	1.1005	271.1
PELT-WT-TCN	1.6752	2.1012	2.2983	0.9806	1.7180	46.8

Two results worth stating plainly. Every one of the five models has Theil's U above 1, so not one of them beats a random walk. And the paper's ranking does not survive: it puts PELT-WT-TCN first, whereas here the TCN comes last by a clear margin. The rest of the order does reproduce — GRU, then multivariate LSTM, then BP&ICSS, then univariate LSTM.

As published in the paper (Table 1, p. 22):

Model	MAE	RMSE	MAPE (%)	R²
BP&ICSS-WT-LSTM	4.6345	5.3878	5.8731	0.8712
PELT-WT-LSTM (uni)	2.3627	2.7488	3.0582	0.9664
PELT-WT-LSTM (multi)	1.8192	2.2967	2.3267	0.9765
PELT-WT-GRU	1.3308	1.6987	1.7401	0.9872
PELT-WT-TCN	1.1855	1.5866	1.6451	0.9888

Available in code as pw.PAPER_TABLE1.

RMSE under all three protocols, so the effect of each change is visible:

Model	Paper	A level	B stationary	C causal
BP&ICSS-WT-LSTM	5.3878	48.8677	1.2847	1.7253
PELT-WT-LSTM (uni)	2.7488	43.3046	1.3459	1.7221
PELT-WT-LSTM (multi)	2.2967	38.2507	1.2615	1.7215
PELT-WT-GRU	1.6987	55.1775	1.2361	1.7269
PELT-WT-TCN	1.5866	37.2711	2.1012	2.2677
Random walk	—	1.2230	1.2230	1.7217

Under protocol A, the paper's specification applied literally, every model lands between RMSE 37 and 55 with R² between −5.1 and −12.4, and the forecast collapses to a flat band around EUR 20 against a truth of EUR 33–98. That is not a bug in this implementation — §6 explains why, and the reasoning is reproducible.

Under protocol C, with every look-ahead removed, all four recurrent models land within 0.3 % of the random walk and of each other. Theil's U is 1.000 to three decimals. The formal tests then settle it:

• Diebold–Mariano, best model vs the random walk: DM = −0.122, p = 0.9027. Not significant. No pairwise difference among the four recurrent models is significant either.
• Model Confidence Set at α = 0.10: five of six models survive, including the random walk. The only specification rejected is the paper's own preferred one, PELT-WT-TCN — rejected for being significantly worse (p = 0.0000).

Once the leak is removed there is no evidence that any of the paper's five architectures forecasts the EUA price better than assuming tomorrow's price equals today's.

Full numbers, and the 34 figures, land in results/ and assets/.

A few of the figures

Structural breaks in the EUA price, matched to the policy chronology (the paper's Figure 7):

Every model's forecast against the realised price on the test window (Figure 14):

Pairwise Diebold–Mariano p-values — the test the paper does not run. Pale cells are pairs that cannot be distinguished:

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6. What the replication found

Four findings, all reproducible. Details and derivations in docs/REPLICATION_NOTES.md.

The models cannot extrapolate past the training range

The EUA price trends hard: the 80 % training window tops out at EUR 35.14 while the test window reaches EUR 98.01 — 2.79× higher. An LSTM or GRU squashes its state through tanh, so once inputs leave the range seen in training the state saturates and the forecast flattens. Measured, 25 epochs:

Configuration	RMSE	R²	Prediction range
one-hot regimes + exogenous (the paper's spec)	55.18	−12.37	EUR 15.4 – 25.9
exogenous only	24.01	−1.53	EUR 32.2 – 69.2
denoised price only	4.42	0.914	EUR 34.3 – 90.5

The more faithful the configuration, the worse it does. stationary=True fixes it by modelling the change instead of the level.

One-hot regime dummies cannot describe a future regime

PELT finds 11 breaks, so 12 regimes. After an 80/20 split, regimes 7–11 occur only in the test window: five of the twelve one-hot columns are identically zero for every training row, so no network can learn a weight for them. This is structural to the paper's e_t encoding — the last regime always begins after the last training observation.

The wavelet filter looks ahead

wavedec/waverec over the whole series is two-sided. Perturbing the price from t = 3000 onwards changes the denoised value as early as t = 2994 — a six-observation look-ahead. For a one-step-ahead forecast, one would already be too many. Use denoise_mode="causal".

The paper never benchmarks against a random walk

On this data the no-change forecast gives RMSE 1.223, R² 0.9934 — better than every model in the paper's Table 1, including the winner (1.5866). Plain OLS on the same 30-step windows reaches RMSE 0.8189. A high R² on a near-unit-root series in levels is not evidence of skill.

Neither Diebold–Mariano nor a Model Confidence Set appears in the paper, so none of its reported differences is shown to be significant. Both are provided here.

Two errata

• The abstract's headline "22.35 % RMSE / 18.63 % MAE" improvement cannot be recovered from the paper's own Table 1. The true figures are 70.55 % / 74.42 % against BP&ICSS-WT-LSTM and 6.60 % / 10.92 % against PELT-WT-GRU; no pair of rows gives 22.35 % / 18.63 %. Check it with pw.improvement_table.
• Training times are reported twice and disagree (Figure 16 vs the Section 4.3 text). Both are kept in pw.PAPER_TRAIN_TIMES.

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7. The real dataset

load_paper_dataset() returns 6,113 rows × 14 columns, exactly the paper's sample size, cached in data/.

Block	Columns
Target	Carbon_Price (EUA spot, EUR/tCO₂)
Energy	Europe_Coal, TTF_Natural_Gas, Henry_Hub_Gas, Brent_Crude
Equity / FX	Euro_Stoxx_50, DAX, VIX, EURUSD
Uncertainty	EPU_US, EPU_UK, GPR, EU_10Y_Yield
Policy	Policy (reconstructed — see below)

Three features named in the paper have no free feed and are listed in pw.UNAVAILABLE_FEATURES: Epex Spot Germany (commercial licence), the Citi Economic Surprise Index (Bloomberg/Citi), and 1-week Euribor (EMMI licence). Epex is the paper's second-ranked driver, so its absence is material.

The Policy feature is never defined in the paper, despite being its most important predictor (Extra-Trees importance > 0.5). build_policy_features reconstructs it transparently from the twelve dated events the paper itself lists in Section 4.1, as a signed exponentially-decaying impulse plus the EU ETS phase number. It is documented as a reconstruction, not the original series.

Your own data works too — any dated frame with a target column:

pipe = pw.PELTWTPipeline(stationary=True).fit(my_df, price_col="Price")

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8. Module map

Module	Contents
peltwtcn/datasets.py	live loaders, caching, the policy reconstruction, POLICY_EVENTS
peltwtcn/breaks.py	PELT, ICSS, Bai–Perron, BP&ICSS, regime encoding
peltwtcn/wavelet.py	decomposition, denoising, causal denoising, thresholds
peltwtcn/features.py	z_t design matrix, sliding windows, scalers
peltwtcn/models.py	LSTM, GRU, TCN, weight-normalised dilated causal conv
peltwtcn/pipeline.py	PipelineConfig, PELTWTPipeline, run_experiment
peltwtcn/metrics.py	MAE/RMSE/MAPE/R²/Theil U, Diebold–Mariano, MCS
peltwtcn/tables.py	Table 1, descriptives, break inventory, paper comparison
peltwtcn/plots.py	every figure of the paper, journal styling

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9. Documentation

Start with the tutorial. It is a single script you can run today, and the guide is its narrative twin.

Document	What it covers
examples/tutorial_step_by_step.py	Start here. A runnable 13-step tutorial, ~5 minutes, printing what every stage produced
docs/TUTORIAL_OUTPUT.md	The verbatim output of that script, so you can check your own run against it
docs/STEP_BY_STEP_GUIDE.md	How to write the code, stage by stage — 15 steps, every block runnable, with the reasoning
docs/SYNTAX.md	Complete API reference: every function, argument and return value
docs/REPLICATION_NOTES.md	What matches the paper, what cannot, and the errata
examples/run_full_replication.py	All three protocols end to end at the paper's own 50-epoch settings

python examples/tutorial_step_by_step.py     # learn it   (~5 min)
python examples/run_full_replication.py      # replicate it (~30 min)

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10. Testing

pytest                          # everything
pytest -m "not slow"            # skip the network fits
pytest -m "not network"         # skip the live downloads

200 fast tests, 13 more that fit networks. Highlights of what is actually verified, rather than merely asserted:

• the TCN's dilated convolution is strictly causal — perturbing x_t for t ≥ 20 leaves every output before t = 20 bit-identical — and matches a hand-rolled reference convolution to float32 precision;
• the wavelet reconstruction identity A + ΣD = f;
• the paper's filter does leak and the causal one does not;
• PELT recovers known break locations to within 5 observations, and ICSS finds a variance shift while ignoring a mean shift;
• Theil's U of a random walk is exactly 1;
• the bundled dataset is 6,113 rows spanning the paper's exact dates;
• the 70.55 % and 6.60 % improvement figures, pinned as regression tests.

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11. Citation

If you use this software, please cite both the implementation and the original paper. A CITATION.cff is included.

@software{roudane2026peltwtcn,
  author  = {Roudane, Merwan},
  title   = {peltwtcn: Hybrid deep-learning carbon price forecasting with
             PELT structural-break detection and wavelet denoising},
  year    = {2026},
  version = {1.0.0},
  url     = {https://github.com/merwanroudane/peltwtcn},
  license = {MIT}
}

@article{ren2025hybrid,
  author  = {Ren, Runsheng and Li, Jing and Li, Yanxiu and Huang, Shixun and
             Shen, Jun and Li, Wanqing and Le, John and Wang, Sheng},
  title   = {A Hybrid Deep Learning based Carbon Price Forecasting Framework
             with Structural Breakpoints Detection and Signal Denoising},
  journal = {arXiv preprint arXiv:2511.04988},
  year    = {2025},
  url     = {https://arxiv.org/abs/2511.04988}
}

Key methodological references

Reference	DOI
Bai & Perron (2003), J. Applied Econometrics	10.1002/jae.659
Inclán & Tiao (1994), JASA	10.2307/2290916
Killick, Fearnhead & Eckley (2012), JRSS-B	10.1111/j.1467-9868.2011.01004.x
Mallat (1989), IEEE TPAMI	10.1109/34.192463
Lin & Zhang (2022), Process Safety and Env. Protection	10.1016/j.psep.2022.08.011
Liu et al. (2012), Energy Economics	10.1016/j.eneco.2011.09.002
Geurts, Ernst & Wehenkel (2006), Machine Learning	10.1007/s10994-006-6226-1
Cho et al. (2014), EMNLP	10.3115/v1/D14-1179
Bai, Kolter & Koltun (2018)	arXiv:1803.01271
Hochreiter & Schmidhuber (1997), Neural Computation	10.1162/neco.1997.9.8.1735

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12. Author

Dr Merwan Roudane

• Email: merwanroudane920@gmail.com
• GitHub: @merwanroudane

Other packages: QuantileOnQuantile, mqqr, qqkrls, mqqcause (CRAN).

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Licence

MIT — see LICENSE.

The implementation is original work. The methodology is due to Ren et al. (2025); please cite them. Redistribution of the underlying price series is subject to each provider's own terms.