On Unlearning for Time-series Forecasting

Zeyu Shi; Yanhui Luo; Ziming Hong; Chongyang Gao; Kezhen Chen; Shanshan Ye; Lixu Wang

cs.LGOct 2, 2026

On Unlearning for Time-series Forecasting

Authors: Zeyu Shi, Yanhui Luo, Ziming Hong, Chongyang Gao, Kezhen Chen, Shanshan Ye, Lixu Wang

Organizations: The Chinese University of Hong Kong, Shenzhen · Zhejiang University · University of Sydney · Northwestern University · Analogy AI, Inc. · Mohamed Bin Zayed University of Artificial Intelligence

Abstract

Time-series forecasting is widely used in sensitive domains. Models in these settings are often trained on longitudinal user- or entity-level records, which may later require removal because they contain sensitive or proprietary information or have been corrupted by sensor failures. To address such deletion requests without costly retraining, machine unlearning has been widely studied as a practical mechanism for privacy protection and data governance. However, the application of machine unlearning to time series prediction has not yet been well realized; this is mainly due to the following unique challenges: Gradient-based unlearning can be unstable because a deleted observation participates in multiple causally connected forecasting windows, causing parameter updates to propagate beyond the requested interval and degrade retained forecasting utility. Label-guided updating offers a more controlled alternative, but continuous and context-dependent forecasts lack a suitable replacement target, while the exact-retrained output is unavailable during unlearning. Moreover, the remaining support for a deleted temporal pattern is highly non-uniform. Some affected windows retain structurally similar counterparts in the retained data, whereas others become underrepresented or isolated. We present RDTU, a Residual Diffusion framework for time-series unlearning. RDTU first uses a retained-set neural tangent kernel predictor to obtain a deletion-compatible base forecast. Then it quantifies the global and local structural support of each affected window using the volume contribution of the retained-reference data. Then a diffusion model generates a residual correction that estimates the counterfactual forecast, yielding a pseudo-label field that guides a lightweight model update. Experiments show that RDTU consistently produces unlearned models that most closely match exact retraining.

Figures & tables

Figure 1: Overview of our proposed time-series unlearning framework RDTU. (1) The retained-set NTK predictor produces a base prediction for the affected window. (2) SIS integrates global directional contribution and local retained support to quantify the structural irreplaceability. (3) Conditioned on the NTK prediction and SIS, the residual diffusion model generates a residual correction. (4) The final label guides the unlearning update.

Method	Univariate Forecasting								Multivariate Forecasting
	Air Quality				Traffic				EEG				HAR70
	$\mathbf{U/N}$	F-P Gap	NRMSE	Time	$\mathbf{U/N}$	F-P Gap	NRMSE	Time	$\mathbf{U/N}$	F-P Gap	NRMSE	Time	$\mathbf{U/N}$	F-P Gap	NRMSE	Time
Original	0.6009	6.56	0.2546	–	0.6454	15.57	0.3941	–	0.6389	5.24	0.1069	–	0.6911	11.96	0.3495	–
Retrain	0.5034	–	0.2622	26.323	0.5291	–	0.3955	12.549	0.5235	–	0.1148	8.910	0.5210	–	0.3459	32.371
SSD	0.5218	52.8954	0.6683	0.946	0.5371	72.6908	0.8928	0.395	0.5180	54.1037	0.5877	0.227	0.5204	72.0281	0.5763	0.623
NegGrad+	0.5090	162.1498	1.5902	9.871	0.5412	140.9170	1.3989	4.340	0.5261	102.1933	0.9080	2.397	0.5372	288.0736	1.6082	10.051

Table 1: Performance comparison between our method and other unlearning baselines on univariate and multivariate forecasting tasks. Unlearning effectiveness is evaluated by the two-sided U/N AUC and the F-P Gap(%), where U/N values closer to

0.5

indicate lower distinguishability between forgotten and never-seen samples, and a lower F-P Gap(%) indicates closer predictive agreement with exact retraining. Forecasting utility is evaluated by test NRMSE, with lower values indicating better predictive performance. Computational efficiency is measured by wall-clock time in seconds.

Methods	Univariate Forecasting						Multivariate Forecasting
	Air Quality			Traffic			EEG			HAR70
	$\mathbf{U/N}$	F-P Gap	NRMSE	$\mathbf{U/N}$	F-P Gap	NRMSE	$\mathbf{U/N}$	F-P Gap	NRMSE	$\mathbf{U/N}$	F-P Gap	NRMSE
w/o Diffusion	0.5250	5.2378	0.2685	0.5455	11.3759	0.3946	0.5297	4.2684	0.1232	0.5190	9.8371	0.3434
Residual-MLP	0.5201	5.0807	0.2632	0.5454	10.3245	0.3940	0.5341	5.5752	0.2583	0.5261	10.064	0.3398
Residual-ARIMA	0.5392	4.9284	0.2609	0.5381	10.7915	0.3968	0.5218	4.2113	0.1135	0.5175	10.8921	0.3498
w/o SIS	0.5180	5.0545	0.2610	0.5475	10.2339	0.3964	0.5226	3.9427	0.1171	0.5213	10.0836	0.3452

Table 2: Ablation study of the key components of our method on different datasets.

Figure 2: Sensitivity analysis of RDTU under different diffusion steps of Horizon Length=1.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Method	Air Quality				Traffic
	U/N	F-P Gap	NRMSE	Time	U/N	F-P Gap	NRMSE	Time
Original	0.6082	10.91	0.4084	–	0.6716	15.57	0.4908	–
Retrain	0.5400	–	0.4131	20.480	0.5478	–	0.5063	12.640
SSD	0.5429	43.31	0.6725	0.77	0.5501	79.35	0.9927	0.450
NegGrad+	0.5356	167.58	1.6929	7.88	0.5346	79.90	0.8708	3.930
Zero-label	0.5348	50.79	0.6918	3.33	0.5507	49.89	0.7294	1.820

Appendix

Table 3: Robustness comparison on univariate datasets under a forecasting horizon of

H=3

. U/N values closer to

0.5

indicate better unlearning effectiveness, while lower F-P Gap, NRMSE, and runtime indicate better performance.

Method	EEG				HAR70
	U/N	F-P Gap	NRMSE	Time	U/N	F-P Gap	NRMSE	Time
Original	0.6759	5.24	0.1986	–	0.6946	12.53	0.3977	–
Retrain	0.5152	–	0.2055	8.980	0.5162	–	0.3975	30.71
SSD	0.5257	59.03	0.6593	0.230	0.5247	82.05	0.6331	0.55
NegGrad+	0.5267	95.88	0.8748	2.350	0.5314	208.95	1.1839	9.28
Zero-label	0.5244	60.22	0.6029	0.360	0.5231	58.71	0.4528	0.62

Appendix

Table 4: Robustness comparison on multivariate datasets under a forecasting horizon of

H=3

. U/N values closer to

0.5

indicate better unlearning effectiveness, while lower F-P Gap, NRMSE, and runtime indicate better performance.

Method	Air Quality				Traffic
	U/N	F-P Gap	NRMSE	Time	U/N	F-P Gap	NRMSE	Time
Original	0.6653	12.39	0.5379	–	0.6645	17.02	0.5821	–
Retrain	0.5330	–	0.5556	16.54	0.5698	–	0.5916	10.94
SSD	0.5312	51.25	0.7903	1.02	0.5661	78.50	0.9965	0.76
NegGrad+	0.5423	105.31	1.1596	7.48	0.5583	53.88	0.7481	3.53
Zero-label	0.5310	50.57	0.7553	4.14	0.5723	49.50	0.7698	2.84

Appendix

Table 5: Robustness comparison on univariate datasets under a forecasting horizon of

H=6

. U/N values closer to

0.5

indicate better unlearning effectiveness, while lower F-P Gap, NRMSE, and runtime indicate better performance.

Method	EEG				HAR70
	U/N	F-P Gap	NRMSE	Time	U/N	F-P Gap	NRMSE	Time
Original	0.7301	10.74	0.3678	–	0.6982	13.88	0.4393	–
Retrain	0.5210	–	0.3770	–	0.5215	–	0.4430	34.45
SSD	0.5268	58.46	0.7230	0.62	0.5187	81.82	0.6467	0.86
NegGrad+	0.5305	93.27	0.9043	2.60	0.5271	182.69	0.9548	9.91
Zero-label	0.5289	56.45	0.6505	0.79	0.5199	59.14	0.4808	1.10

Appendix

Table 6: Robustness comparison on multivariate datasets under a forecasting horizon of

H=6

. U/N values closer to

0.5

indicate better unlearning effectiveness, while lower F-P Gap, NRMSE, and runtime indicate better performance.

Figure 3: Sensitivity analysis of RDTU under different diffusion steps of Horizon Length=3. The curves report the F-P Gap and the time cost of diffusion.

Figure 4: Sensitivity analysis of RDTU under different loss-weight ratios

\lambda_{\mathrm{f}}/\lambda_{\mathrm{r}}

of Horizon Length=1. The curves report the mean test NRMSE and F-P Gap, while the shaded regions indicate the corresponding standard errors over 30 runs. Lower values indicate better performance for both metrics.

Explore similar work

Can You Delete a Year of Market Data? Machine Unlearning Against Exact Retraining Oracles
Aug 13, 2026Junyi YeMachine Unlearning Machine Unlearning Evaluation
School of Computing, Montclair State University Montclair, New Jersey, USA
DFMU: Data-Frugal Machine Unlearning
Jun 24, 2026Sajith U, Prateek KeserwaniMachine Unlearning
Samsung R&D Institute India-Bangalore, India
Efficient Unlearning with Privacy Guarantees
Jul 7, 2025Josep Domingo-Ferrer, Najeeb Jebreel, David SánchezPrivacy-Preserving ML Machine Unlearning
1CYBERCAT (Center for Cybersecurity Research of2026 Catalonia), ComSCIAM-Center for Computational Science and Applied Mathematics, Department of Computer EngineeringJun and Mathematics, Universitat Rovira i Virgili, Av. Pa¨ısos26 Catalans 26, E-43007 Tarragona, Catalonia

Aug 13, 2026J/K move · Enter open · S save

Can You Delete a Year of Market Data? Machine Unlearning Against Exact Retraining Oracles

Junyi Ye

School of Computing, Montclair State University Montclair, New Jersey, USA

Machine Unlearning Machine Unlearning Evaluation Time Series Forecasting

Open paper AskPDF arXiv

When a data license expires, deleting stored records does not remove influence encoded in a trained forecaster. Machine unlearning seeks to remove this influence without retraining. We benchmark temporal unlearning with 3,200 paired references trained on all data and oracles retrained without the requested period. The grid covers five architectures, four rolling folds, five deletable years, and three experimental deletion levels on an S&P 500 volatility panel. The 2020 COVID crisis year produces the largest memorization gap for every architecture. Removing it improves all three deployable models in every fold, with the largest improvement in the 2022 bear market, while the two non-deployable models respond inconsistently. The target for approximate unlearning is the oracle, not low predictive accuracy on the deleted period. In one Transformer cell, an oracle that never trained on 2020 still predicts it at an information coefficient of 0.51, compared with 0.55 for the reference; pushing predictions toward noise reduces test skill. Across twelve deployable architecture-method pairs, only TSMixer with the hinge method remains near the oracle in every fold, closing 74-118% of the reference-to-oracle gap without a measurable loss of test skill. Method rankings vary across architectures and rolling windows. Audit separation rises with prior memorization but can remain small after exact deletion. The window-level loss comparison reaches at most 0.69, and treating stock-level windows as independent inflates the absolute t-statistic by a median factor of 1.9. These results call for an explicit deletion scope, oracle validation for the relevant architecture and window, and power-aware auditing.

Abstract

Explore similar work

Can You Delete a Year of Market Data? Machine Unlearning Against Exact Retraining Oracles

DFMU: Data-Frugal Machine Unlearning

Efficient Unlearning with Privacy Guarantees