DBCM: Dual-Branch Calibration Module for Test-Time Adaptation in Time Series Forecasting

Jaebyeong Jeon; Kunwoo Kang; Sang Yup Lee; Kibok Lee

cs.LGOct 23, 2026

DBCM: Dual-Branch Calibration Module for Test-Time Adaptation in Time Series Forecasting

Authors: Jaebyeong Jeon, Kunwoo Kang, Sang Yup Lee, Kibok Lee

Organizations: Department of Statistics and Data Science, Yonsei University · Digital Analytics, College of Computing, Yonsei University · Department of Communication, Yonsei University

Abstract

Non-stationarity induces test-time distribution shifts in time series forecasting (TSF), resulting in forecast residuals between predictions and the corresponding ground truth. Recent works on test-time adaptation for TSF address this by introducing lightweight calibration modules around frozen forecasters, updated using observations that become incrementally available at test time. Existing approaches typically employ channel-wise adapters, implicitly assuming that forecast residuals are inherently channel-specific. However, we observe that forecast residuals often exhibit substantial shared structure across channels, suggesting that fully independent channel-wise parameterization may be redundant. Motivated by this observation, we propose the Dual-Branch Calibration Module (DBCM), which shares adaptation capacity across channels through a shared adapter while retaining limited channel-specific flexibility through a low-rank channel-wise adapter, further enhanced by channel mixing and nonlinear gated modulation. Extensive experiments show that DBCM consistently outperforms prior methods across diverse datasets, horizons, and backbones.

Figures & tables

Panel of Figure 1 — Figure 1: Shared Structure in Forecast Residuals. Visualization on ETTh1 with iTransformer as the source forecaster. While raw channels are heterogeneous, forecast residuals exhibit structured patterns across channels. This suggests that independent channel-wise correction may be redundant.

Figure 2: Overview of the Dual-Branch Calibration Module (DBCM). Given an input sequence, DBCM first applies channel mixing and processes the mixed sequence with a shared adapter and a channel-wise LoRA adapter. Their outputs are combined with a bias term, modulated by nonlinear gating, and added through a residual path to produce the calibrated sequence. The same DBCM structure is used on the output-side to calibrate the forecast.

Table 1: Channel-Space Analysis. Channel-space concentration of forecast residuals across backbones and datasets, and the subspace alignment between forecast residuals and adapter corrections.

		iTransformer				DLinear				FreTS
		Baseline	TAFAS	PETSA	DBCM	Baseline	TAFAS	PETSA	DBCM	Baseline	TAFAS	PETSA	DBCM
ETTh1	96	.4349	.4308	.4284	.4228	.4510	.4425	.4400	.4318	.4360	.4295	.4296	.4242
	192	.4937	.4894	.4886	.4805	.5042	.4946	.4943	.4835	.4886	.4819	.4842	.4764
	336	.5406	.5382	.5392	.5322	.5508	.5454	.5455	.5373	.5466	.5394	.5462	.5354
	720	.6914	.6520	.6535	.6298	.7019	.6713	.6617	.6487	.7145	.6839	.6795	.6565
ETTh2	96	.2430	.2406	.2403	.2388	.2294	.2274	.2280	.2268	.2376	.2347	.2359	.2347

Table 2: Prediction Performance Comparison Across Methods. Test MSE is reported for six models on six datasets with four prediction horizons. Bold entries indicate the best performance among methods, while underlined entries denote the second-best. Avg. Imp. denotes the relative MSE reduction (%) over the frozen baseline, averaged over all dataset–horizon settings. Full results with standard deviations are provided in Table C.14 .

Electricity
	Baseline	TAFAS	PETSA	DBCM
iTransformer	.1828	.1770	.1798	.1744
DLinear	.2149	.2093	.2118	.2063
FreTS	.1978	.1936	.1956	.1924
TSFMs
Moirai	.5039	.3470	.3507	.3238

Table 3: Scalability. Average test MSE on Electricity (over four horizons) and on TSFMs (over the four ETT datasets at

H=96

Panel of Figure 3 — Figure 3: Ablation Study. (a) Component ablation with test MSE (across datasets and horizons) and parameter counts under incremental component addition. (b) Effect of LoRA rank on test MSE.

Appendix figures & tables22 assets

Supplementary material from the paper’s appendix.

Appendix

Figure A.1: Effect of Channel Mixing on Residual Structure. Visualization of forecast residuals for the same test window, from left to right: the original forecast residual, the residual after applying the learned channel mixer adapted during TSF-TTA, and the residual after applying an oracle channel mixer optimized for that window. MSE and

\mathrm{EVR}@2

are reported in each panel.

Figure A.2: Channel-Wise Relative Improvement. Channel-wise relative MSE improvement over the iTransformer, comparing the shared-only DBCM variant with the full DBCM using both shared and channel-wise LoRA branches. The overall column reports the relative MSE improvement over all channels.

Figure A.3: Qualitative Analysis. Visualization of forecasting examples on ETTh1, ETTm1, ETTh2, and Exchange Rate using iTransformer as the source forecaster. The figure compares the frozen source forecaster and TSF-TTA methods, including TAFAS, PETSA, and DBCM.

Signal	$\mathrm{EVR}@2$	$\mathrm{Rank}@90$
Source, low-order desc.	0.854	2.89
Source, freq./temporal desc.	0.728	4.11
Source, all desc.	0.652	5.17
Previous, all desc.	0.596	5.67

Appendix

Table A.1: Raw Data Drift Spectra.

\mathrm{EVR}@k

: top-

k

explained variance ratio;

\mathrm{Rank}@90

: minimum rank explaining 90% variance.

Dataset	TAFAS	TAFAS-Shared	PETSA	DBCM
ETTh1	0.772	0.812	0.649	0.874
ETTh2	0.648	0.676	0.679	0.684
ETTm1	0.876	0.893	0.824	0.897
ETTm2	0.707	0.858	0.787	0.875
Exchange	0.457	0.554	0.533	0.603
Weather	0.566	0.543	0.521	0.712

Appendix

Table A.2: Dataset-Wise Residual–Correction Alignment. Projection similarity between the top-2 channel subspaces of forecast residuals and adapter corrections.

Dataset	$C$	$\mathrm{EVR}@30\%$	$\mathrm{Rank}@90/C$
Weather	21	98.2	27.4
Electricity	321	83.2	45.3

Appendix

Table A.3: Residual Spectrum on High-Dimensional Data. Centered channel-space metrics of forecast residuals, reported in %.

	iTransformer				DLinear				FreTS
	Baseline	TAFAS	PETSA	DBCM	Baseline	TAFAS	PETSA	DBCM	Baseline	TAFAS	PETSA	DBCM
96	.1452	.1426	.1446	.1415	.1974	.1897	.1924	.1844	.1745	.1682	.1704	.1663
192	.1692	.1588	.1612	.1584	.1971	.1907	.1930	.1886	.1814	.1767	.1782	.1766
336	.1765	.1719	.1752	.1706	.2117	.2059	.2089	.2051	.1973	.1931	.1957	.1923
720	.2402	.2346	.2382	.2271	.2534	.2508	.2530	.2471	.2380	.2363	.2379	.2345
Avg.	.1828	.1770	.1798	.1744	.2149	.2093	.2118	.2063	.1978	.1936	.1956	.1924

Appendix

Table C.1: Prediction Performance Comparison on the Electricity Dataset. Test MSE is reported for iTransformer, DLinear and FreTS across four prediction horizons.

	ETTh1	ETTh2	ETTm1	ETTm2
Moirai	.4917	.2650	1.0543	.2044
+ TAFAS	.4740	.2557	.4720	.1862
+ PETSA	.4816	.2628	.4708	.1875
+ DBCM	.4629	.2524	.4010	.1788
Chronos	.5316	.2553	1.5167	.2242
+ TAFAS	.4811	.2467	.4252	.1866

Appendix

Table C.2: TSF-TTA on TSFMs. Test MSE of TSF-TTA methods evaluated on Moirai, Chronos, and Chronos-2 for horizon

H=96

		iTransformer			DLinear			FreTS
		Baseline	DynaTTA	DBCM	Baseline	DynaTTA	DBCM	Baseline	DynaTTA	DBCM
ETTh1	96	.4349	.5253	.4228	.4510	.4632	.4318	.4360	.5199	.4242
	192	.4937	.5608	.4805	.5042	.5161	.4835	.4886	.5505	.4764
	336	.5406	.5979	.5322	.5508	.5687	.5373	.5466	.6277	.5354
	720	.6914	.7576	.6298	.7019	.7080	.6487	.7145	.9315	.6565
ETTh2	96	.2430	.3498	.2388	.2294	.2305	.2268	.2376	.2523	.2347

Appendix

Table C.3: Prediction Performance Comparison with DynaTTA. Test MSE is reported for three backbone models on six datasets with four prediction horizons. Bold entries indicate the best performance among methods, while underlined entries denote the second-best.

		iTransformer				DLinear				FreTS
		Baseline	COSA-F	COSA-P	DBCM	Baseline	COSA-F	COSA-P	DBCM	Baseline	COSA-F	COSA-P	DBCM
ETTh1	96	.4349	.4325	.4326	.4272	.4510	.4437	.4433	.4354	.4360	.4324	.4326	.4261
	192	.4937	.4920	.4913	.4790	.5042	.4977	.4997	.4867	.4886	.4875	.4877	.4769
	336	.5406	.5388	.5322	.5177	.5508	.5458	.5420	.5274	.5466	.5433	.5383	.5213
	720	.6914	.6452	.6229	.5738	.7019	.6635	.6425	.5853	.7145	.6768	.6573	.6054
ETTh2	96	.2430	.2418	.2408	.2391	.2294	.2285	.2281	.2273	.2376	.2371	.2364	.2359

Appendix

Table C.4: Prediction Performance Comparison with COSA. Test MSE obtained by applying the update protocol used in COSA. Bold entries indicate the best performance among methods, while underlined entries denote the second-best.

		iTransformer
		Baseline	DynaME	DBCM
ETTh1	96	.4349	.4370	.4228
	192	.4937	.4933	.4805
	336	.5406	.5509	.5322
	720	.6914	.7008	.6298
ETTh2	96	.2430	.2379	.2388

Appendix

Table C.5: Prediction Performance Comparison with DynaME. Test MSE is reported for iTransformer on six datasets with four prediction horizons. Bold entries indicate the best performance among methods, while underlined entries denote the second-best.

Figure C.1: Prediction Performance under Different Normalization Settings. Test MSE of the source forecaster without TSF-TTA and with TAFAS, PETSA, or DBCM across prediction horizons. The three panels correspond to settings without an additional normalization module (w/o Norm.), with RevIN, and with DDN, respectively. For each horizon, results are averaged over six source forecasters and six datasets. Lower values indicate better performance.

		iTransformer				DLinear				FreTS
		Baseline	TAFAS	PETSA	DBCM	Baseline	TAFAS	PETSA	DBCM	Baseline	TAFAS	PETSA	DBCM
ETTh1	96	.4385	.4380	.4372	.4365	.4540	.4509	.4519	.4486	.4402	.4378	.4381	.4364
	192	.5053	.5042	.5048	.5033	.5146	.5114	.5129	.5095	.5019	.5001	.5002	.4990
	336	.5689	.5686	.5690	.5678	.5783	.5771	.5768	.5749	.5753	.5738	.5738	.5734
	720	.7714	.7589	.7711	.7644	.7765	.7606	.7758	.7694	.7898	.7771	.7893	.7831
ETTh2	96	.2476	.2463	.2459	.2458	.2348	.2342	.2346	.2343	.2445	.2430	.2418	.2418

Appendix

Table C.6: Prediction Performance Comparison in TTFBench. Test MSE evaluated on TTFBench is reported for three source forecasters on six datasets with four prediction horizons. Bold entries indicate the best performance among methods, while underlined entries denote the second-best.

Method	Param. Ratio (%)	Peak mem (MB)	Samples/sec	Adapt. time (ms)	Infer. time (ms)	Average MSE
TAFAS	16.00	512.04	12022.58	12.93	8.30	0.3531
PETSA	1.14	491.04	11814.63	14.47	8.89	0.3556
DBCM	5.63	492.78	12339.85	15.23	8.77	0.3444

Appendix

Table C.7: Computational Efficiency Comparison. Summary of adapter parameter ratio, memory usage, throughput, adaptation time, inference time, and average MSE across TSF-TTA methods. Param. Ratio denotes the number of additional adapter parameters relative to the number of parameters of the source forecaster.

Method	Param. Ratio (%)	Peak mem (MB)	Samples/sec	Adapt. time (ms)	Infer. time (ms)	Average MSE
TAFAS	74.98	2109.64	2594.97	28.64	10.05	0.1770
PETSA	25.04	1672.08	2567.59	26.77	10.28	0.1799
DBCM	28.80	2143.44	2710.95	26.09	9.34	0.1744

Appendix

Table C.8: Computational Efficiency on Electricity. Results are averaged over the four forecasting horizons for the iTransformer forecaster.

Method	Param. Ratio (%)	Peak mem (MB)	Samples/sec	Adapt. time (ms)	Infer. time (ms)	Average MSE
TAFAS	0.0635	4604.39	669.64	163.85	90.68	0.3349
PETSA	0.0126	4603.04	664.87	172.88	93.09	0.3504
DBCM	0.0286	4604.26	670.41	164.92	90.91	0.3176

Appendix

Table C.9: Computational Efficiency on Chronos. Results are averaged over ETTh1, ETTh2, ETTm1, and ETTm2 with three random seeds.

		iTransformer				DLinear				FreTS
		Baseline	Input	Output	Both	Baseline	Input	Output	Both	Baseline	Input	Output	Both
ETTh1	96	.4349	.4326	.4223	.4228	.4510	.4379	.4288	.4318	.4360	.4315	.4242	.4242
	192	.4937	.4890	.4805	.4805	.5042	.4888	.4828	.4835	.4886	.4850	.4760	.4764
	336	.5406	.5320	.5326	.5322	.5508	.5405	.5372	.5373	.5466	.5405	.5353	.5354
	720	.6914	.6886	.6321	.6298	.7019	.6716	.6484	.6487	.7145	.7055	.6565	.6565
ETTh2	96	.2430	.2407	.2378	.2388	.2294	.2260	.2276	.2268	.2376	.2346	.2355	.2347

Appendix

Table C.10: Prediction Performance Comparison by Adaptation Side. Test MSE is reported for three backbone models on six datasets with four prediction horizons. Bold entries indicate the best performance among methods, while underlined entries denote the second-best.

	ETTh1	ETTh2	ETTm1	ETTm2	Exchange	Weather	Electricity
Linear	.5163	.3135	.4339	.2190	.3413	.2424	.1744
MLP	.5182	.3124	.4381	.2182	.3410	.2424	.1756
Attention	.5278	.3184	.4458	.2215	.3767	.2449	.1753
Uniform	.5212	.3146	.4431	.2213	.3726	.2453	.1746

Appendix

Table C.11: Ablation on Channel Mixing. Test MSE across datasets under different channel mixing strategies. Bold entries indicate the best performance among the compared variants.

	ETTh1	ETTh2	ETTm1	ETTm2	Exchange	Weather	Electricity
Sigmoid	.5163	.3135	.4339	.2190	.3413	.2424	.1744
ReLU	.5278	.3148	.4435	.2204	.3692	.2458	.1756
SiLU	.5323	.3154	.4450	.2207	.3718	.2454	.1748
Tanh	.5200	.3150	.4400	.2205	.3631	.2462	.1743

Appendix

Table C.12: Ablation on Nonlinear Gating Function. Test MSE across datasets under different nonlinear gating functions. Bold entries indicate the best performance among the compared variants.

Bias parameterization	ETTh1	ETTh2	ETTm1	ETTm2	Exchange	Weather	Electricity
Full ( $\mathbb{R}^{L\times C}$ )	.5166	.3136	.4340	.2190	.3412	.2422	.1744
Channel-wise ( $\mathbb{R}^{C}$ )	.5163	.3135	.4339	.2190	.3413	.2424	.1744
Time-wise ( $\mathbb{R}^{L}$ )	.5168	.3136	.4344	.2190	.3413	.2423	.1744
Scalar ( $\mathbb{R}$ )	.5167	.3136	.4344	.2190	.3414	.2424	.1745
None	.5168	.3136	.4345	.2190	.3414	.2424	.1744

Appendix

Table C.13: Ablation on Bias Parameterization. Test MSE under different additive bias parameterizations. Here,

L

and

C

denote the temporal length and number of channels, respectively. Bold entries indicate the best performance among the compared variants.

Dataset	Domain	Frequency	# Channels	Description
Electricity	Electricity	1 hour	321	Hourly electricity consumption from 2012 to 2014.
Weather	Weather	10 minutes	21	Meteorological indicators recorded every 10 minutes in 2020.
ETTh	Electricity	1 hour	7	Hourly transformer load and oil-temperature data.
ETTm	Electricity	15 minutes	7	15-minute transformer load and oil-temperature data.
Exchange	Finance	1 day	8	Daily exchange rates from eight countries.

Appendix

Table D.1: Benchmark Dataset Characteristics. We summarize the domain, sampling frequency, number of channels, and a brief description of each dataset.

Dataset	Time Steps	ADF
ETTh1	17,420	-5.91
ETTm1	69,680	-14.98
ETTh2	17,420	-4.13
ETTm2	69,680	-5.66
Exchange	7,588	-1.90
Weather	52,696	-26.68

Appendix

Table D.2: Benchmark Dataset Statistics. We report the number of time steps and ADF test statistic for each dataset.

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