Robust Residual Correction via Selective Deployment for Time Series Forecasting

Jianxiang Xie; Yuncheng Hua; Mingyue Cheng; Flora D. Salim; Hao Xue

cs.LGDec 27, 2025

Robust Residual Correction via Selective Deployment for Time Series Forecasting

Authors: Jianxiang Xie, Yuncheng Hua, Mingyue Cheng, Flora D. Salim, Hao Xue

Organizations: School of Computer Science and Engineering, University of New South Wales, Sydney, Australia · State Key Laboratory of Cognitive Intelligence, School of Computer Science and Technology, University of Science and Technology of China, Hefei, China · The Hong Kong University of Science and Technology (Guangzhou)

Abstract

Post-hoc residual correction can reduce forecasting error, but always-on updates often fail to generalize: when residual signals are weak or noisy, expressive correctors can overfit and even increase the overall forecasting errors. We introduce CRC, a robust residual correction framework that couples a hybrid corrector with a validation-calibrated selective deployment rule. CRC proposes corrections via a conservative ridge "floor" plus conditional nonlinear refinement, but deploys them only when held-out evidence indicates net error reduction over a frozen baseline forecaster. CRC treats when to revise a forecast as a validation-calibrated deployment decision, not only how to fit residuals. Across standard long-sequence benchmarks and multiple backbones, CRC improves horizon-averaged MSE and MAE in most dataset-backbone pairs, with particularly large gains on complex datasets (e.g., over 20% relative MSE reduction on Traffic). We additionally report the non-degradation rate (NDR) as a stability diagnostic of harmful updates and ablate the validation-calibrated "firewall" that stabilizes MSE gains.

Figures & tables

Figure 1: Overview of the CRC framework. CRC first extracts structured residual representations, then proposes conservative and conditional correction components, and finally applies a validation-calibrated deployment rule that deploys corrections only when held-out evidence supports them.

Dataset	Model	MSE (Baseline)	MSE (CRC)	Imp MSE (%)	MAE (Baseline)	MAE (CRC)	Imp MAE (%)
ETTh1	DLinear	0.4603	0.4582	0.46	0.4568	0.4554	0.29
	PatchTST	0.4478	0.4468	0.22	0.4476	0.4454	0.50
	TimeXer	0.4441	0.439	1.14	0.4451	0.444	0.24
	TimesNet	0.4565	0.4562	0.06	0.4528	0.4525	0.06
ETTh2	DLinear	0.5641	0.5383	4.57	0.5194	0.497	4.32
	PatchTST	0.3807	0.3794	0.35	0.4092	0.4078	0.36

Table 1: Horizon-averaged MSE and MAE improvements of CRC across datasets and backbones (averaged over horizons 96, 192, 336, 720). Improvements are relative to the baseline and positive values indicate gains. Full horizon-wise results are reported in Appendix Table 7 .

Config	B1 MAE	B1 MSE	B1 NDR	B2 MAE	B2 MSE	B2 NDR	B3 MAE	B3 MSE	B3 NDR
G0 Baseline	0.4108	0.3962	—	0.4654	0.4874	—	0.2184	0.1685	—
G1 Always-on	0.4738	0.4665	8.2	0.5689	0.6328	10.6	0.2326	0.1803	33.9
G2 Ridge+val gate	0.4097	0.3941	97.9	0.4693	0.4920	97.1	0.2111	0.1626	90.0
G3 No dir gate	0.4079	0.3865	81.8	0.4684	0.4786	78.5	0.2098	0.1611	81.5
G4 Deploy-only	0.4097	0.3941	62.1	0.4592	0.4838	77.8	0.2081	0.1584	79.4
G5 Full CRC	0.3914	0.3780	80.3	0.4392	0.4612	79.7	0.1903	0.1408	78.5

Table 3: Controlled deployment ladder (G0–G5) on B1–B3 (seed 2021). B1/B2/B3: ETTh1+DLinear at pred_len 96/336 and Weather+TimesNet at 96. Not horizon-averaged like Table 1 . G0 baseline, G1 always-deploy (blend search off;

\tau

/direction gate retained), G2 ridge+validation gate only (no MLP), G3 w/o direction gate, G4 deploy-only encoder, G5 full CRC. Lower MAE/MSE and higher NDR (%) are better.

Dataset	TimeXer	TimesNet	PatchTST	DLinear	Winner
ETTh1	$-0.0223$	$0.0000$	$-0.0036$	$-0.0217$	pir
ETTh2	$-0.0076$	$0.0053$	$0.0141$	$-0.1673$	crc
ETTm1	$0.0116$	$0.0116$	$0.0042$	$-0.0065$	crc
ETTm2	$0.0205$	$0.0138$	$0.0102$	$-0.0537$	crc
Weather	$0.0117$	$0.0192$	$0.0371$	$0.0267$	crc
Electricity	$0.0066$	$-0.0001$	$0.0123$	$0.0154$	crc

Table 4: Horizon-averaged relative forecasting error differences between PIR and CRC (

\Delta=\mathrm{PIR}-\mathrm{CRC}

; positive indicates CRC better). Winner summarizes the majority sign of

\Delta

across backbone–horizon pairs for each dataset. Full horizon-wise results (including MAE) are reported in Appendix Table 8 .

Figure 2: NDR stability curves. Non-degradation rate (NDR, %) of PIR vs. CRC across horizons on Weather and ETTm2 (higher is better). Each panel corresponds to one backbone; annotations report mean $\Delta$ NDR in percentage points (pp). Exact values are provided in Appendix Table 5 .

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Backbone	Horizon	PIR	CRC
DLinear	96	87.7	88.2
	192	75.7	93.7
	336	79.1	89.5
	720	59.8	90.4
PatchTST	96	78.5	82.5
	192	80.1	87.0

Appendix

Weather

Backbone	Horizon	PIR	CRC
DLinear	96	67.4	90.0
	192	62.2	79.5
	336	48.8	87.2
	720	42.3	83.0
PatchTST	96	77.5	81.1
	192	65.9	81.9

Appendix

ETTm2

Robust Time Series Forecasting

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Open paper AskPDF arXiv

Time series forecasting models are increasingly deployed in continuously evolving environments. After a forecast is issued, future observations gradually arrive and reveal how the model has failed. Existing methods mainly treat such observations as supervision for parameter updates. However, it remains unclear whether verified forecasting errors can themselves provide causal feedback for correcting future predictions. To address this, we introduce Error Feedback Calibration (EFC), a fully test-time framework for deterministic post-hoc correction of time series forecasting. EFC constructs a Causal Error Diagonal (CED) from revealed errors of overlapping historical forecasts, providing a fresh view of the frozen forecaster's recent failure behavior. Then Cumulative Error Transport (CET) maps this error state to future residuals using cumulative estimation, while temporal out-of-sample validation controls the correction strength. Temporal Residual Learning (TRL) further predicts only the residual structure left after CET from recent CED trajectories, rather than relearning the entire forecasting error. Extensive experiments across forecasting backbones and datasets show that EFC broadly improves forecasting performance while substantially controlling harmful over correction.

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