DrafTS: Time-Aware Decomposition with Residual Correction for Time Series Modeling

Yiqiu Liu; Siru Zhong; Zhiguang Wang; Qingsong Wen; Yuxuan Liang

cs.AISep 27, 2026

DrafTS: Time-Aware Decomposition with Residual Correction for Time Series Modeling

Authors: Yiqiu Liu, Siru Zhong, Zhiguang Wang, Qingsong Wen, Yuxuan Liang

Organizations: The Hong Kong University of Science and Technology (Guangzhou), China · Abel AI Lab, USA · Squirrel Ai Learning, USA

Abstract

Real-world time series contain evolving underlying dynamics with irregular variations that lack stable temporal patterns and are often referred to as noise. Existing methods address this mixture by filtering frequencies or suppressing noisy observations. They either miss temporal evolution or risk suppressing useful dynamics. We propose DrafTS, a model-agnostic framework that aims to reduce noise while preserving evolving dynamics through time-aware Decomposition with ResiduAl correction For Time Series. DrafTS uses features derived from instantaneous amplitude and frequency to guide decomposition into a primary component intended to capture underlying dynamics. A task-specific backbone models the primary component, while a lightweight correction module uses residual information to correct the backbone output. Across four time series modeling tasks, DrafTS improves six diverse backbones, demonstrating its effectiveness. Code is at https://github.com/Autumn61q/DrafTS

Figures & tables

Figure 1: Modeling paradigms for underlying dynamics and noise. (a) Frequency-wise filtering overlooks temporal evolution. (b) Observation-wise suppression limits learning from noisy observations, suppressing useful dynamics within them. (c) Time-Aware Decomposition with Correction tracks evolving dynamics and exploits dynamics left in the residual.

Figure 2: EMD and Hilbert transform example. The first five IMFs are shown. Applying the Hilbert transform to

c_{5}(t)

yields

z_{5}(t)

and its instantaneous amplitude and frequency. Re and Im denote real and imaginary parts; orange markers mark time

t^{*}

Figure 3: Overview of DrafTS . Right: Time-aware decomposition splits $x_{1:T}$ into the primary component $\mathbf{s}^{\prime}$ and residual $\mathbf{r}^{\prime}$ . The backbone and Residual-Aware Correction (RC) produce the base output and residual correction, respectively, which are summed to obtain $\mathbf{o}$ . Left: Enlarged view of the blue shaded box showing how analytic features are mapped to time-aware masks for each IMF.

Tasks	Datasets	Metrics	Series Length
Forecasting	Long-term: ETTh1, ETTm1, Weather, Electricity, ILI, ECG, Laser, Noisy Lorenz63 (SNR={3,5,7})	MSE, MAE	$16\sim 720$
Forecasting	Short-term: M4 (6 subsets)	sMAPE, MASE, OWA	$6\sim 48$
Classification	UEA (10 subsets)	Accuracy	$29\sim 1152$
Anomaly Detection	SMD, MSL, SMAP, SWaT, PSM	Precision, Recall, F1-Score	100

Table 1: Summary of the experiment datasets. Further details are provided in Appendix A.1 .

Figure 4: Samples from Noisy Lorenz63 (SNR=3). Clean and observed data with abrupt events are shown alongside analytic features derived from the first IMF of the observed data.

Dataset

Metric

Crossformer ( 2023 )

PatchTST ( 2023 )

iTransformer ( 2023 )

TimeMixer ( 2024a )

TimeFilter ( 2025 )

L-Drive ( 2026 )

Raw

+ DrafTS

Raw

+ DrafTS

Raw

+ DrafTS

Raw

+ DrafTS

Raw

+ DrafTS

Raw

+ DrafTS

ETTh1

MSE

0.449

0.443 (

+

1.34%)

0.459

0.457 (

+

0.44%)

0.448

0.440 (

+

1.79%)

0.458

0.453 (

+

1.09%)

0.488

0.475 (

+

2.66%)

0.472

0.465 (

+

1.48%)

MAE

0.445

0.441 (

+

0.90%)

0.432

0.431 (

+

0.23%)

0.431

0.431 (

+

0.00%)

0.429

0.428 (

+

0.23%)

0.457

0.453 (

+

0.88%)

0.447

0.443 (

+

0.89%)

ETTm1

MSE

0.413

0.401 (

+

2.91%)

0.396

0.392 (

+

1.01%)

0.400

0.394 (

+

1.50%)

0.393

0.385 (

+

2.04%)

0.385

0.386 (-0.26%)

0.383

0.376 (

+

1.83%)

MAE

0.404

0.400 (

+

0.99%)

0.387

0.386 (

+

0.26%)

0.390

0.389 (

+

0.26%)

0.385

0.383 (

+

0.52%)

0.385

0.386 (-0.26%)

0.383

0.382 (

+

0.26%)

Weather

MSE

0.241

0.239 (

+

0.83%)

0.251

0.247 (

+

1.59%)

0.268

0.263 (

+

1.87%)

0.283

0.241 (

+

14.84%)

0.238

0.235 (

+

1.26%)

0.237

0.234 (

+

1.27%)

Table 2: Long- and short-term forecasting results. Results are averaged over horizons per dataset, with weighted averages over six M4 subsets. Gray cells indicate + DrafTS , Bold red marks the better result within each raw/augmented pair. Full results are in Table 13 and Table 14 .

Figure 5: Classification and anomaly detection results. Full results see Table 15 and Table 16 .

Residual Module	MSE	MAE	Trainable	Total
No Correction	0.815	0.655	–	–
RC (ours)	0.805 (0.001)	0.653 ( $<$ 0.001)	12.48K	16.77K
Flatten Linear	0.815( $<$ 0.001)	0.661( $<$ 0.001)	55.49K	55.49K
Trainable RC	0.809 (0.009)	0.656 (0.006)	16.77K	16.77K

Table 3: Residual correction on Crossformer. Noisy Lorenz63 (SNR

=7

dB,

S=64

); mean(std) over three head seeds. Trainable/Total: trainable/stored parameters.

Method	AUC		Minimum Error
Method	MSE	MAE	MSE	MAE
Ours ( DrafTS )	0.340	0.309	0.319 (5.49%)	0.291 (2.26%)
FFT-high	0.352	0.321	0.322 (1.28%)	0.293 (1.28%)
FFT-low	0.403	0.358	0.347 (1.38%)	0.310 (1.38%)
DCT-high	0.362	0.331	0.344 (4.01%)	0.310 (4.01%)
STFT-high	0.363	0.331	0.333 (6.30%)	0.301 (6.30%)

Table 4: Decomposition Comparison. TimeFilter test errors on noisy Lorenz63. AUC is normalized over the common energy-reduction range; parentheses give the reduction at minimum error. See Appendix A.3 for the full protocol.

Dataset	Raw	Raw + RC	Analyt. + [Amp., Freq., $O$ ]	Analyt. + $\phi$	Analyt. + [Amp., Freq., $O$ ] + RC	DrafTS (Ours)
SNR=3	0.699 / 0.505	0.713 / 0.527	0.713 / 0.522	0.716 / 0.520	0.702 / 0.511	0.674 / 0.489
SNR=5	0.648 / 0.513	0.636 / 0.502	0.663 / 0.522	0.667 / 0.526	0.602 / 0.474	0.595 / 0.470
SNR=7	0.604 / 0.509	0.561 / 0.470	0.600 / 0.500	0.548 / 0.464	0.529 / 0.445	0.522 / 0.438

Table 5: Ablation results on Noisy Lorenz63. Each entry reports MSE / MAE averaged over

S=16,64

. Analyt. denotes the analytic IMFs. Full results see Appendix B.5 .

Method	Params.	Peak Alloc. (MiB)	Train Iters.	MSE	MAE	Model FLOPs/Sample
Raw	4,836,628	197.24	570	3.848	1.055	0.21179 GFLOPs
+ DrafTS	4,847,553	198.54	440	2.785	0.978	0.21204 GFLOPs
Change vs. Raw	$\uparrow 0.23\%$	$\uparrow 0.66\%$	$\downarrow 22.81\%$	$\downarrow 27.62\%$	$\downarrow 7.30\%$	$\uparrow 0.12\%$

Table 6: Efficiency comparison. Analytic signals are precomputed offline.

Figure 6: Qualitative Visualization. DrafTS (blue) and backbone (dashed light blue) predictions, with ground truth (dark navy) and observed inputs (gray).

Dataset	Residual Magnitude (%)	Residual Variance	Temporal-Variation Alignment
ETTm1	1.74	0.292	0.240
ILI	3.70	0.370	0.484

Table 7: Decomposition adaptivity. Temporal-variation alignment is the Pearson correlation between residual energy and local temporal variation.

Figure 7: Hyperparameter sensitivity. Relative MSE changes use

J=1

in (a) and reservoir size 16 in (b) as references within each SNR.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Dim	Input Length	Prediction Length	Dataset Size	Frequency / Information
ETTh1	7	96	$\{96,192,336,720\}$	$(8640,2880,2880)$	Hourly / Temperature
ETTm1	7	96	$\{96,192,336,720\}$	$(34560,11520,11520)$	15 min / Temperature
Electricity	321	96	$\{96,192,336,720\}$	$(18412,2630,5262)$	Hourly / Electricity
Weather	21	96	$\{96,192,336,720\}$	$(36887,5269,10540)$	10 min / Meteorology
ILI	7	24	$\{24,36,48,60\}$	$(676,96,194)$	Weekly / Health
ECG	1	360	$\{144,288\}$	$(7000,1000,2000)$	500 Hz / Health

Appendix

Table 8: Long-term forecasting dataset descriptions. Sizes are reported as (train, validation, test).

Dataset	Dim	Input Length	Prediction Length	Official Series (Train, Test)	Frequency / Information
M4-Yearly	1	12	6	$(23{,}000,23{,}000)$	Yearly / Demographic
M4-Quarterly	1	16	8	$(24{,}000,24{,}000)$	Quarterly / Finance
M4-Monthly	1	36	18	$(48{,}000,48{,}000)$	Monthly / Industry
M4-Weekly	1	26	13	$(359,359)$	Weekly / Macro
M4-Daily	1	28	14	$(4{,}227,4{,}227)$	Daily / Micro
M4-Hourly	1	96	48	$(414,414)$	Hourly / Other

Appendix

Table 9: Short-term forecasting dataset descriptions. Sizes are reported as (train, test). M4 does not provide official validation splits; validation subsets are constructed exclusively from their official training splits as described in the experimental setup.

Dataset	Samples (Train, Test)	Variables	Series Length
Handwriting	(150, 850)	3	152
LSST	(2459, 2466)	6	36
NATOPS	(180, 180)	24	51
RacketSports	(151, 152)	6	30
SelfRegulationSCP2	(200, 180)	7	1152
CharacterTrajectories	(1422, 1436)	3	60–182

Appendix

Table 10: UEA classification datasets. Validation sets are split from the official training sets.

Dataset	Dataset sizes (train, val, test)	Variable Number	Sliding Window Length
SMD	(566724, 141681, 708420)	38	100
MSL	(44653, 11664, 73729)	55	100
SMAP	(108146, 27037, 427617)	25	100
SWaT	(396000, 99000, 449919)	51	100
PSM	(105984, 26497, 87841)	25	100

Appendix

Table 11: Anomaly detection dataset descriptions. Sizes are reported as (train, val, test).

Method	Scanned settings	Runs	Used
DrafTS	11 paired $(m_{\max},m_{\rm init})$ settings	11	10
FFT-high	cutoff $\{0.4,0.6\}$ ; energy target $10^{-4}$ – $0.2$	10	8
FFT-low	fraction $\{0.4,0.6,0.8\}$ ; energy target $10^{-4}$ – $0.2$	11	8
DCT-high	cutoff $\{0.4,0.6\}$ ; energy target $10^{-4}$ – $0.2$	10	8
STFT-high	cutoff $\{0.5,0.6\}$ ; window 24; overlap 0.75	9	7
FFT-adap	mask maximum $0.1$ – $0.212$ ; energy target $3{\times}10^{-5}$ – $0.02$	7	4

Appendix

Table 12: Search grids used for Table 4. “Used” denotes the number of operating points within the common energy-reduction interval. Different grid sizes reflect method-specific mappings from control settings to realized energy reduction; nAUC is computed over the same common interval.

Dataset	Horizon	Crossformer				PatchTST				iTransformer				TimeMixer				TimeFilter				L-Drive
		( 2023 )				( 2023 )				( 2023 )				( 2024a )				( 2025 )				( 2026 )
		Raw		+ DrafTS		Raw		+ DrafTS		Raw		+ DrafTS		Raw		+ DrafTS		Raw		+ DrafTS		Raw		+ DrafTS
		MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETTh1	96	0.394	0.404	0.383	0.397	0.394	0.392	0.393	0.392	0.384	0.391	0.380	0.391	0.401	0.395	0.392	0.394	0.419	0.423	0.416	0.422	0.401	0.406	0.388	0.402
	192	0.436	0.431	0.424	0.423	0.447	0.423	0.447	0.423	0.438	0.422	0.431	0.420	0.443	0.420	0.442	0.420	0.482	0.449	0.458	0.444	0.449	0.429	0.447	0.429
	336	0.471	0.453	0.471	0.450	0.490	0.444	0.488	0.443	0.487	0.446	0.475	0.446	0.492	0.441	0.484	0.440	0.499	0.456	0.494	0.456	0.499	0.458	0.489	0.452

Appendix

Table 13: Full long-term forecasting results on seven real-world datasets and Noisy Lorenz63 at three noise levels with and without DrafTS . Gray rows report the relative improvement (

\Delta

) achieved by DrafTS , where higher values are better.

Subset	Metric	Crossformer [-2pt] ( 2023 )		PatchTST [-2pt] ( 2023 )		iTransformer [-2pt] ( 2023 )		TimeMixer [-2pt] ( 2024a )		TimeFilter [-2pt] ( 2025 )		L-Drive [-2pt] ( 2026 )
Subset	Metric	Raw	$+$ DrafTS	Raw	$+$ DrafTS	Raw	$+$ DrafTS	Raw	$+$ DrafTS	Raw	$+$ DrafTS	Raw	$+$ DrafTS
Yearly	sMAPE	15.369	15.059	13.926	13.859	14.076	14.023	15.343	15.169	13.996	14.032	14.076	13.896
	MASE	3.571	3.442	3.177	3.125	3.169	3.159	3.450	3.368	3.115	3.111	3.177	3.102
	OWA	0.919	0.894	0.826	0.817	0.829	0.827	0.904	0.888	0.820	0.821	0.830	0.815
Quarterly	sMAPE	11.467	11.588	10.640	10.664	10.834	10.741	12.686	12.048	11.289	10.971	11.151	10.899
	MASE	1.302	1.369	1.257	1.257	1.260	1.251	1.552	1.460	1.326	1.264	1.371	1.306

Appendix

Table 14: Full short-term forecasting results on M4 with and without DrafTS . Gray cells report the results obtained with DrafTS and the corresponding relative improvement.

Dataset	Crossformer ( 2023 )		PatchTST ( 2023 )		iTransformer ( 2023 )		TimeMixer ( 2024a )		TimeFilter ( 2025 )		L-Drive ( 2026 )
Dataset	Raw	+ DrafTS	Raw	+ DrafTS	Raw	+ DrafTS	Raw	+ DrafTS	Raw	+ DrafTS	Raw	+ DrafTS
Handwriting	18.98	19.02	19.84	21.14	11.76	18.35	4.59	5.45	9.45	10.67	9.22	9.45
LSST	51.55	53.61	54.07	53.73	57.91	58.57	56.27	56.34	60.34	60.84	54.41	55.08
NATOPS	73.33	75.00	74.07	75.00	80.19	80.37	31.11	43.52	77.96	78.70	29.26	38.15
RacketSports	71.93	73.03	63.38	66.23	70.18	76.97	50.44	51.10	61.62	63.16	58.55	60.09
SelfRegulationSCP2	55.00	55.19	48.15	49.07	51.30	55.74	48.89	49.26	51.85	50.56	50.56	51.11

Appendix

Table 15: Full classification results on 10 UEA datasets with and without DrafTS averaged over three seeds. The better result in each Raw/+ DrafTS pair is highlighted in bold red .

Dataset	Metric	Crossformer ( 2023 )		PatchTST ( 2023 )		iTransformer ( 2023 )		TimeMixer ( 2024a )		TimeFilter ( 2025 )		L-Drive ( 2026 )
Dataset	Metric	Raw	+ DrafTS	Raw	+ DrafTS	Raw	+ DrafTS	Raw	+ DrafTS	Raw	+ DrafTS	Raw	+ DrafTS
SMD	Precision	56.08	64.26	70.92	71.27	72.72	74.46	66.52	67.56	63.14	70.91	70.87	70.98
	Recall	88.47	87.70	89.22	88.33	87.84	88.01	89.85	89.98	89.05	87.70	88.38	88.43
	F1	68.64	74.14	79.03	78.89	79.56	80.67	76.44	77.13	73.81	78.37	78.65	78.75
MSL	Precision	82.38	82.43	80.58	79.96	79.75	79.86	81.15	80.97	80.17	81.89	81.27	80.25
	Recall	87.91	87.91	87.27	88.22	88.22	88.22	87.27	88.58	87.74	87.63	87.27	87.74

Appendix

Table 16: Full anomaly detection results on five datasets with and without DrafTS , averaged over three seeds. The better result in each Raw/+ DrafTS pair is highlighted in bold red .

Dataset	Horizon	Raw	Raw + RC	Analyt. + [Amp., Freq., $O$ ]	Analyt. + $\phi$	Analyt. + [Amp., Freq., $O$ ] + RC	DrafTS (Ours)
SNR=3	16	0.551 / 0.391	0.578 / 0.426	0.582 / 0.427	0.546 / 0.389	0.524 / 0.378	0.508 / 0.363
SNR=3	64	0.848 / 0.620	0.849 / 0.628	0.843 / 0.617	0.886 / 0.651	0.880 / 0.645	0.839 / 0.616
SNR=5	16	0.508 / 0.415	0.451 / 0.369	0.499 / 0.408	0.490 / 0.399	0.412 / 0.333	0.411 / 0.332
SNR=5	64	0.788 / 0.611	0.821 / 0.635	0.827 / 0.635	0.843 / 0.652	0.792 / 0.615	0.778 / 0.608
SNR=7	16	0.414 / 0.377	0.329 / 0.298	0.420 / 0.380	0.363 / 0.334	0.324 / 0.295	0.320 / 0.289
SNR=7	64	0.795 / 0.640	0.794 / 0.641	0.781 / 0.621	0.733 / 0.594	0.734 / 0.596	0.724 / 0.586

Appendix

Table 17: Detailed ablation results on Noisy Lorenz63. Each entry reports MSE / MAE for TimeFilter at seed 42. Analyt. denotes the analytic IMFs.

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Sep 30, 2026, cs.LGJ/K move · Enter open · S save

WinoTS: Wavelet-based Self-Distillation for Time Series Models

Noam Major, Kathy Razmadze, Yoli Shavit

Bar-Ilan University, Ramat-Gan, Israel

Time Series Wavelets Equivariant Learning Data Augmentation

Open paper AskPDF arXiv

Self-supervised pre-training of time series models is currently dominated by next-token prediction and reconstruction objectives. In continuous-valued domains, these paradigms often waste model capacity on high-frequency, point-wise noise at the expense of learning invariant structure. While invariance-based self-distillation has proven highly effective in computer vision, its application to temporal data remains largely underexplored. Effectively adapting such methods to time series requires carefully designed augmentations: spatial operations like cropping can shift the timing of repeating cycles or distort the signal, while basic jittering may provide limited variation. We introduce Wavelet-based self-distillation for time series (WinoTS), an invariance-based pre-training paradigm designed specifically for temporal signals. At its core, WinoTS leverages time-frequency augmentations to construct multi-scale structural views without distorting underlying signal dynamics. Across extensive evaluations, WinoTS outperforms state-of-the-art baselines in long-term forecasting, cross-domain zero-shot transfer, and unsupervised anomaly detection. Notably, linear probing on frozen WinoTS representations frequently surpasses fully supervised models trained from scratch. Systematic ablations demonstrate that WinoTS is a flexible, architecture-agnostic framework yielding gains across time series backbones, and establish that time-frequency transformations provide a principled alternative to vision-style spatial augmentations.

Abstract

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WinoTS: Wavelet-based Self-Distillation for Time Series Models

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