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

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

arXiv:2610.32071v1cs.LGstat.ML

TL;DR

Non-stationarity shifts test-time forecasting distributions, while existing adaptation methods often model residual corrections independently by channel despite shared residual structure. DBCM combines shared adaptation with limited low-rank channel-specific flexibility, and consistently improves performance across evaluated settings, reducing MSE by 6.20% relative to the frozen forecaster across 144 settings.

  • Problem

    Existing TSF-TTA methods typically use independent channel-wise adapters, although forecast residuals often share structure across channels and test-time updates rely on limited sequentially revealed observations.

    Source: §1 · pp. 1–2

  • Method

    DBCM combines a shared adapter with a low-rank channel-wise adapter, enhanced by channel mixing and nonlinear gated calibration.

    Source: §1 · p. 2

  • Results

    Across 144 settings, DBCM consistently improves performance across evaluated backbones, reducing MSE by 6.20% relative to the frozen forecaster, compared with 4.07% for TAFAS and 2.61% for PETSA.

    Source: §5.2 · p. 8

  • Takeaways & Limitations

    Residuals concentrate along a small number of shared channel directions, supporting shared adaptation with low-rank channel-specific flexibility as an effective TSF-TTA inductive bias.

    Source: §6 · p. 9

    The analysis focuses on output-space residuals and corrections and does not explicitly characterize input-side dynamics.

    Source: §6 · p. 9

Abstract

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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.

1 INTRODUCTION

Non-stationarity challenges forecasting, and test-time adaptation uses revealed observations to adjust calibration modules around frozen forecasters. Because residuals can share structure across channels, DBCM combines shared adaptation with limited channel-specific flexibility; the paper reports consistent gains across diverse settings.

1 INTRODUCTION

  • Test-time distribution shifts can degrade pre-trained forecasters, while TSF-TTA uses ground truth revealed after prediction to update lightweight calibration modules around frozen forecasters.The introduction distinguishes this direct test-time supervision from common computer-vision TTA based on entropy minimization over unlabeled inputs.Source: §1 · p. 1
  • Forecast residuals often exhibit substantial shared structure across channels, suggesting that fully independent channel-wise parameterization may be redundant.The paper frames this as a research question because calibration modules learn online from limited, sequentially revealed observations.Source: §1 · p. 2
  • DBCM combines a shared adapter with a low-rank channel-wise adapter, and adds channel mixing and nonlinear gated calibration for input-dependent modulation.The shared branch captures common correction patterns while the low-rank branch retains flexibility for channel-specific residual variations.Source: §1 · p. 2
  • DBCM consistently outperforms existing TSF-TTA methods across diverse datasets, forecasting horizons, and backbone architectures while remaining relatively parameter-efficient.The introduction reports these results across diverse settings without giving specific benchmark values.Source: §1 · p. 2

2 RELATED WORK

Prior TSF-TTA methods use different calibration strategies, including gated calibration, low-rank adapters, dynamic shift estimation, and context-aware output correction. DBCM addresses the shared structure in residuals by combining shared and channel-specific adaptation.

2 RELATED WORK

  • TAFAS uses partially observed ground truth with gated calibration, PETSA uses low-rank input- and output-calibration adapters with dynamic gating, DynaTTA estimates shifts to adjust adaptation rates, and COSA corrects residuals with a context-aware output adapter.The passage identifies these methods as existing TSF-TTA approaches.Source: §2 · pp. 2–3
  • Existing methods rely on channel-wise calibration, while residuals often exhibit shared low-dimensional structure that may make such designs over-parameterized.The passage notes that DBCM instead decomposes adaptation into shared and channel-specific components.Source: §2 · p. 3
  • DBCM reduces redundant channel-wise capacity while retaining flexibility through a low-rank formulation.Its overview shows channel mixing followed by shared and channel-wise LoRA branches, with nonlinear gating and a residual path; the same structure calibrates the forecast.Source: §2 · p. 3, Figure 2 · p. 3

3 METHOD

TSF-TTA adapts calibration modules from sequentially revealed test observations while keeping the source forecaster frozen. DBCM combines shared and low-rank channel-specific corrections with cross-channel mixing and nonlinear gating.

3.1 PROBLEM SETTING

  • Only calibration modules adapt on the sequential test stream; the source forecaster stays frozen, and targets become partially observable as future steps are revealed.All methods use the same evaluation protocol, with MSE computed on adjusted predictions.Source: §3.1 · p. 3

3.2 DUAL-BRANCH CALIBRATION MODULE

  • Input-side DBCM calibrates shifted inputs before the frozen forecaster, while output-side DBCM adjusts its predictions toward the evolving test distribution.The input-side module maps test inputs closer to the forecaster’s training input distribution.Source: §3.2 · p. 3
  • A channel mixer supplies cross-channel context, and a shared temporal transformation applies the same correction parameters to every channel.The mixer helps expose shared latent structure; the shared adapter is designed to capture common corrections with fewer parameters than fully channel-wise adapters.Source: §3.2 · p. 4
  • A low-rank channel-wise branch models residual channel-specific variation, while an input-dependent nonlinear gate modulates the combined correction before channel-wise scaling.The inner gate modulates correction values; the outer tanh gate controls their overall channel-wise contribution.Source: §3.2 · pp. 4–5

4 ANALYSIS

Forecast residuals concentrate in shared channel directions, though that concentration varies by dataset; adapter corrections align with those residual patterns, with DBCM showing the strongest alignment.

Channel-Space Analysis Protocol

  • The analysis stacks residuals and adapter corrections across evaluated instances into channel-space matrices, then compares their spectra and leading subspaces.Alignment is measured between the top-k principal channel directions of residuals and corrections.Source: §4 · p. 5

Forecast Residual Structure

  • Across backbones, residuals have EVR@30% values around 93% and Rank@90/C around 42%, unlike isotropic residuals at 33–43% and 90–100%.These spectra indicate that dominant correction patterns are largely shared across channels.Source: §4 · p. 6, Table 1 · p. 6
  • Weather shows the strongest concentration (EVR@30% 98.2%; Rank@90/C 27.4%), while Exchange Rate shows the weakest (85.7%; 50.0%).Exchange Rate still has structure, but some residual variation lies outside the dominant shared directions.Source: §4 · p. 6

Residual–Correction Alignment

  • TAFAS-Shared aligns more strongly with residuals than TAFAS (0.723 vs. 0.671), while DBCM has the strongest alignment among compared methods.Oracle alignment is 1 by construction; all compared methods exceed the random-subspace baseline.Source: §4 · p. 6, Table 1 · p. 6

5 EXPERIMENTS

Across diverse forecasting settings, DBCM outperforms prior test-time adaptation methods; scalability and ablations examine its behavior across model and data scales and its component choices.

5.2 MAIN RESULTS

  • Across 144 settings, DBCM reduces MSE by 6.20% versus the frozen forecaster, ahead of TAFAS (4.07%) and PETSA (2.61%).The relative MSE reductions are averaged over all dataset–horizon settings.Source: Table 2 · p. 7, §5.2 · p. 8

5.1 EXPERIMENTAL SETUP

  • Setup spans six benchmarks, diverse forecasters, and TSFMs; fixed L=96, four horizons, MSE, and three seeds, with Electricity added for high-dimensional scalability.The six standard benchmarks are ETTh1, ETTh2, ETTm1, ETTm2, Exchange Rate, and Weather.Source: §5.1 · pp. 7–8

5.3 SCALABILITY ACROSS MODEL AND DATA SCALES

  • On Electricity, DBCM leads across backbones and horizons; at iTransformer H=720 it improves the baseline by 5.45%, versus 2.33% for TAFAS and 0.83% for PETSA, and leads on TSFMs.Table 3 reports average test MSE on Electricity over four horizons and on TSFMs over four ETT datasets at H=96.Source: Table 3 · p. 8, §5.3 · p. 8

5.4 ABLATION STUDY

  • Replacing TAFAS’s channel-wise adapter with a shared adapter gives comparable performance with fewer parameters; adding LoRA, channel mixing, and nonlinear gating successively improves the final design.The final design outperforms TAFAS while using fewer parameters.Source: Figure 3 · p. 9, §5.4 · p. 9
  • Performance improves as LoRA rank rises from 2 to 8, but larger ranks add no gains and settings such as 64 or full rank can degrade performance.The results indicate a need for some channel-specific flexibility, but not unrestricted rank.Source: §5.4 · p. 9, Figure 3 · p. 9

6 CONCLUSION

DBCM is motivated by shared structure in forecast residuals and combines shared adaptation with low-rank channel-specific flexibility. The conclusion identifies input-side dynamics as an open area for analysis.

6 CONCLUSION

  • Forecast residuals concentrate along a few shared channel directions, and DBCM combines shared adaptation with a lightweight low-rank branch for channel-specific flexibility.The conclusion presents shared adaptation with low-rank channel-specific flexibility as an effective inductive bias for TSF-TTA.Source: §6 · p. 9
  • The analysis focuses on output-space residuals and corrections, leaving input-side dynamics uncharacterized; direct analysis of input-level adaptation remains future work.The input-side DBCM alone improves forecasting performance, but its adaptation dynamics are not directly analyzed.Source: §6 · pp. 9–10

A.1 EFFECT OF CHANNEL MIXING ON RESIDUAL STRUCTURE.

  • On ETTm2, learned channel mixing lowers MSE from 0.4361 to 0.0991 and raises EVR@2 from 0.731 to 0.769; the oracle reaches 0.0475 MSE and 0.815 EVR@2.The learned mixer reorganizes channel information before correction, yielding a smaller residual target concentrated along fewer channel directions.Source: Figure A.1 · p. 13, §A.1 · p. 13

A.2 EFFECT OF THE CHANNEL-WISE LORA ADAPTER.

  • Across datasets, adding the channel-wise LoRA branch improves most channels over the source forecaster and can turn negative shared-only improvements positive.The full DBCM also outperforms the shared-only variant in overall relative MSE improvement across datasets.Source: §A.2 · p. 13

A.3 QUALITATIVE ANALYSIS.

Qualitative examples with iTransformer show DBCM forecasts closer to ground truth across several datasets, with improvements varying by temporal pattern.

A.3 QUALITATIVE ANALYSIS.

  • On ETTh1 and ETTm1, DBCM better captures local peaks and follows the ground-truth shape; on ETTh2, it more closely matches the target’s scale.The examples compare DBCM with the frozen source forecaster and other TSF-TTA methods.Source: §A.3 · p. 13
  • On Exchange Rate, DBCM predictions align more closely with ground truth when the baseline and competing methods struggle to capture the trend.The examples span local peaks, scale changes, and trend shifts.Source: §A.3 · p. 14

A.4 RAW DATA DRIFT SPECTRA.

The appendix contrasts raw-data drift with forecast-residual structure, then examines correction alignment, high-dimensional residuals, and DBCM’s calibration components.

A.4 RAW DATA DRIFT SPECTRA.

  • Source-referenced low-order drift reaches EVR@2 = 0.854 and Rank@90 = 2.89, but combined descriptors have lower EVR@2 and higher Rank@90 under both references.The combined-descriptor EVR@2 values are 0.652 for the source reference and 0.596 for the previous-window reference; Rank@90 values are 5.17 and 5.67, respectively.Source: §A.4 · pp. 14–15, Table A.1 · p. 15
  • Raw drift descriptors compare test windows with either training-window means or the immediately preceding test window, separating low-order statistics from frequency and temporal patterns.The descriptor families distinguish changes in mean, variance, and slope from changes in spectral energy, periodicity, and autocorrelation.Source: §A.4 · p. 14

A.5 DATASET-WISE RESIDUAL–CORRECTION ALIGNMENT.

  • DBCM corrections have the highest average top-2 residual–correction subspace alignment, 0.774, and the highest alignment on all six datasets.TAFAS-Shared also has higher average alignment than TAFAS and leads it on five of six datasets.Source: §A.5 · p. 15, Table A.2 · p. 16

A.6 RESIDUAL SPECTRUM ON HIGH-DIMENSIONAL DATA.

  • On Electricity, the top 30% of channel directions explain 83.2% of residual variance versus 30.2% for isotropic residuals; 90% is explained by 45.3% of directions versus 90.0%.Residuals remain far from isotropic despite weaker concentration than on Weather.Source: §A.6 · pp. 15–16, Table A.3 · p. 16

B ALGORITHM OF DBCM

  • DBCM’s calibration block combines shared and channel-wise LoRA adapters, nonlinear gated modulation, and a channel-gated residual update.Source: B ALGORITHM OF DBCM · p. 17

C.1 FULL RESULTS ON ELECTRICITY AND TSFMS

Across the reported benchmarks, DBCM performs strongly against competing adaptation methods, including on Electricity, other forecasting models, and normalization settings. Comparisons with DynaTTA, COSA, and DynaME further examine its performance under different methods or update protocols.

C.1 FULL RESULTS ON ELECTRICITY AND TSFMS

  • On Electricity, DBCM achieves the best performance across backbones and horizons; on ETTm1 at H = 96, it reduces Moirai MSE from 1.0543 to 0.4010 and Chronos MSE from 1.5167 to 0.3862.For iTransformer on Electricity at H = 720, DBCM’s gain is 5.45%, compared with 2.33% for TAFAS and 0.83% for PETSA.Source: §C.1 · pp. 17–18, Table C.1 · p. 18, Table C.2 · p. 18

C.2 COMPARISON WITH DYNATTA

  • Across evaluated settings, DBCM consistently achieves the best performance, while DynaTTA often increases forecasting error relative to the frozen baseline.The authors note that the official DynaTTA implementation has reproducibility issues and use the COSA configuration for comparison.Source: §C.2 · p. 18, Table C.3 · p. 19

C.3 COMPARISON WITH COSA

  • Under COSA’s update protocol, DBCM achieves the best average performance across the three evaluated backbones.The authors flag that protocol as exposing the adapter to future target values unavailable in streaming forecasting, so they exclude it from the main experiments.Source: §C.3 · p. 19, Table C.4 · p. 20

C.4 COMPARISON WITH DYNAME

  • With iTransformer, DBCM has the lowest average MSE, 0.3444, compared with 0.3687 for the baseline and 0.3614 for DynaME.DBCM reduces error over the baseline in all 24 dataset–horizon settings and achieves the best performance on all six datasets at the longest horizon.Source: §C.4 · p. 20, Table C.5 · p. 21

C.5 COMPARISON WITH NORMALIZATION METHODS

  • Across six forecasters and six datasets, DBCM has the lowest test MSE across prediction horizons and all three normalization settings: no additional normalization, RevIN, and DDN.TSF-TTA reduces test MSE relative to the corresponding source forecaster in all three settings.Source: §C.5 · pp. 20–21, Figure C.1 · p. 21

C.6 EVALUATION ON TTFBENCH

On TTFBench’s harsher synthesized test-time shifts, DBCM improves robustness across forecasters, while its efficiency profile remains favorable in standard and large-scale settings.

C.6 EVALUATION ON TTFBENCH

  • 0.3825 vs. 0.4068 (DLinear average MSE) and 0.3782 vs. 0.3999 (FreTS average MSE); DBCM also ranks best for iTransformer at 1.42.For iTransformer, its average MSE is slightly higher than TAFAS, driven mainly by Exchange Rate at the longest horizon.Source: Table C.6 · p. 22, §C.6 · p. 22

C.7 COMPUTATIONAL EFFICIENCY

  • DBCM achieves the best predictive performance with a substantially smaller parameter ratio than TAFAS; PETSA has the smallest ratio but the highest average MSE.Across methods, memory, throughput, adaptation time, and inference time are broadly comparable; DBCM’s adaptation time is 0.76 ms longer than PETSA and 2.30 ms longer than TAFAS.Source: §C.7 · pp. 22–23, Table C.7 · p. 23

C.8 COMPUTATIONAL EFFICIENCY IN LARGE-SCALE SETTINGS

  • On 321-channel Electricity, DBCM has the lowest MSE and latency and highest throughput; on Chronos, it has the lowest MSE and highest throughput.The channel-wise LoRA branch scales linearly with channel count, while the shared adapter and nonlinear gate are shared across channels.Source: Table C.8 · p. 23, §C.8 · p. 23, Table C.9 · p. 24

C.9 ABLATION OF INPUT- AND OUTPUT-SIDE DBCM

The ablations find that using DBCM on both input and output sides performs best, while the default linear mixer, sigmoid gate, and channel-wise bias offer simple effective choices.

C.9 ABLATION OF INPUT- AND OUTPUT-SIDE DBCM

  • Combining input- and output-side DBCM achieves the best average performance across all three backbones, with the two adaptation sides serving complementary roles.Input calibration mitigates distribution shift before forecasting, while output calibration corrects residual prediction errors afterward.Source: Table C.10 · p. 24, §C.9 · p. 24
  • Both single-side variants improve over the frozen baseline; output-side calibration generally gives stronger gains, though DLinear slightly favors input-side average MSE.Input-side calibration targets mismatch before the forecaster processes the test window.Source: Table C.10 · p. 24, §C.9 · p. 24

C.10 ABLATION ON CHANNEL MIXING

  • Performance differences across mixing strategies are small; the default linear mixer is comparable to alternatives without their added complexity.MLP’s marginal MSE gains on ETTh2, ETTm2, and Exchange Rate do not consistently transfer; attention offers no clear advantage, and uniform mixing is generally less effective than linear mixing.Source: Table C.11 · p. 25, §C.10 · p. 25

C.11 ABLATION ON THE NONLINEAR GATING FUNCTION

  • Sigmoid gives the lowest MSE on every dataset except Electricity, where Tanh is marginally better at 0.1743 versus 0.1744.ReLU, SiLU, and Tanh do not provide a consistent advantage over Sigmoid across the remaining datasets.Source: Table C.12 · p. 25, §C.11 · p. 25

C.12 ABLATION ON BIAS PARAMETERIZATION

  • Performance differences among bias parameterizations are small, and the default channel-wise bias performs comparably to the alternatives.The full, time-wise, scalar, and no-bias variants yield similar results across datasets.Source: §C.12 · p. 25, Table C.13 · p. 26

D DETAILED DATASET INFORMATION

The benchmark datasets span a wide range of non-stationarity, assessed using the ADF statistic as a proxy for evolving temporal dynamics.

D DETAILED DATASET INFORMATION

  • ADF values closer to zero indicate stronger non-stationarity, but the statistic does not directly measure train–test distribution discrepancy.Exchange has the highest reported ADF value (−1.90), while Weather has a highly negative value (−26.68).Source: D DETAILED DATASET INFORMATION · p. 26
  • The benchmark datasets cover a wide range of non-stationarity, with Exchange identified as the strongest and Weather as relatively stable.The ADF values cited for these datasets are −1.90 and −26.68, respectively.Source: D DETAILED DATASET INFORMATION · p. 26
  • The appendix presents dataset domains, temporal resolutions, channel counts, and brief descriptions alongside stationarity statistics.These statistics include the number of time steps and ADF test values.Source: D DETAILED DATASET INFORMATION · p. 26

E TRAINING SETUP

The appendices specify a consistent training and tuning setup, describe channel-wise drift descriptors, and position DBCM within forecasting, adaptation, and cross-channel research.

E TRAINING SETUP

  • Backbones are pretrained for 30 epochs, and all adaptation methods receive the same hyperparameter tuning budget and selection procedure.Experiments use three seeds per backbone configuration and a single RTX 4090 GPU, except Moirai, Chronos, and Chronos-2 experiments, which use an RTX 6000 ADA.Source: E TRAINING SETUP · p. 26

F DRIFT DESCRIPTORS

  • Six channel-wise drift descriptors cover mean, log-variance, slope, dominant frequency, spectral-band energy, and autocorrelation.The descriptor families are compared with source-training-window or immediately preceding test-window references.Source: F DRIFT DESCRIPTORS · pp. 28–29

G ADDITIONAL RELATED WORK

  • Related work spans forecasting architectures, general test-time adaptation, cross-channel modeling, and online learning for time series.The paper distinguishes its frozen-forecaster setting, where only external calibration modules are updated.Source: G ADDITIONAL RELATED WORK · pp. 29–31
  • Low-rank residual structure is treated as an empirical hypothesis, not a universal property; its strength can vary across datasets and forecasters.This motivates combining shared parameters with a channel-wise LoRA branch for limited channel-specific flexibility.Source: G ADDITIONAL RELATED WORK · p. 30

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