CoRA: Boosting Time Series Foundation Models for Multivariate Forecasting through Correlation-aware Adapter

Hanyin Cheng; Xingjian Wu; Yang Shu; Zhongwen Rao; Lujia Pan; Bin Yang; Chenjuan Guo

cs.LGMar 23, 2026

CoRA: Boosting Time Series Foundation Models for Multivariate Forecasting through Correlation-aware Adapter

Authors: Hanyin Cheng, Xingjian Wu, Yang Shu, Zhongwen Rao, Lujia Pan, Bin Yang, Chenjuan Guo

Organizations: East China Normal University · Huawei Noah’s Ark Lab

Abstract

Most existing Time Series Foundation Models (TSFMs) use channel independent modeling and focus on capturing and generalizing temporal dependencies, while neglecting the correlations among channels or overlooking the different aspects of correlations. However, these correlations play a vital role in Multivariate time series forecasting. To address this, we propose a CoRrelation-aware Adapter (CoRA), a lightweight plug-and-play method that requires only fine-tuning with TSFMs and is able to capture different types of correlations, so as to improve forecast performance. Specifically, to reduce complexity, we innovatively decompose the correlation matrix into low-rank Time-Varying and Time-Invariant components. For the Time-Varying component, we further design learnable polynomials to learn dynamic correlations by capturing trends or periodic patterns. To learn positive and negative correlations that appear only among some channels, we introduce a novel dual contrastive learning method that identifies correlations through projection layers, regulated by a Heterogeneous-Partial contrastive loss during training, without introducing additional complexity in the inference stage. Extensive experiments on 10 real-world datasets demonstrate that CoRA can improve TSFMs in multivariate forecasting performance.

Figures & tables

Figure 1: (a) Illustration of three different types of correlations, the formal definitions are provided in Appendix A . (b) Comparisons of different plugins for learning correlations

Figure 2: The framework of CoRA. (a) CoRA begins by learning DCorr in Dynamic Correlation Estimation module. Heterogeneous Division module projects representations into positive and negative spaces for HCorr. Then CoRA conducts H-PCorr Contrastive Learning in each space to guide projection and capture PCorr. (b) The DCorr Estimation module estimates correlations by combining Rule-based Correlations and Learnable Correlations, which are computed by Time-aware Polynomial and Time-Varying and Time-Invariant (T-T) Composition. (c) H-PCorr contrastive learning minimizes distances between strongly correlated channels and maximizes separation between weakly correlated channels in both positive and negative spaces.

Figure 3: The details of DCorr Estimation

Model	LLM-based						Pre-trained
Model	GPT4TS (2023)		CALF (2025)		UniTime (2024)		Moment (2024)		Timer (2024)		TTM (2024)
Plugin	✗	✓	✗	✓	✗	✓	✗	✓	✗	✓	✗	✓
ETTh1	0.468	0.456	0.443	0.434	0.739	0.714	0.550	0.543	0.444	0.432	0.405	0.397
ETTh2	0.375	0.362	0.373	0.367	0.399	0.386	0.370	0.365	0.356	0.350	0.343	0.340
ETTm1	0.389	0.379	0.373	0.364	0.408	0.394	0.455	0.452	0.360	0.356	0.357	0.353
ETTm2	0.279	0.269	0.272	0.264	0.292	0.281	0.279	0.275	0.262	0.257	0.259	0.254

Table 1: Multivariate forecasting results in the 5% few-shot setting with MSE are averaged across four different forecasting horizons

H\in\{96,192,336,720\}

.The better results are highlighted in bold . Full and MAE results are available in Appendix E .

Panel of Figure 4 — Figure 4: Correlation Plugins comparison in 5% few-shot fine-tuning setting.

Panel of Table 2 — Table 2: The MSE results of various variants.

Panel of Figure 5 — Figure 5: Efficiency Analysis of TSFMs with and without the application of CoRA.

Dataset	ETTm2				Weather
Data	3%	5%	10%	20%	3%	5%	10%	20%
TTM	0.263 $\pm.005$	0.259 $\pm.003$	0.256 $\pm.003$	0.250 $\pm.002$	0.237 $\pm.003$	0.226 $\pm.002$	0.224 $\pm.002$	0.216 $\pm.001$
+ CoRA	0.261 $\pm.004$	0.254 $\pm.002$	0.248 $\pm.001$	0.245 $\pm.001$	0.234 $\pm.003$	0.224 $\pm.002$	0.212 $\pm.001$	0.210 $\pm.001$
CALF	0.285 $\pm.005$	0.272 $\pm.003$	0.268 $\pm.004$	0.261 $\pm.003$	0.251 $\pm.004$	0.238 $\pm.002$	0.230 $\pm.003$	0.224 $\pm.002$
+ CoRA	0.283 $\pm.003$	0.264 $\pm.002$	0.260 $\pm.002$	0.254 $\pm.002$	0.248 $\pm.003$	0.231 $\pm.002$	0.223 $\pm.002$	0.219 $\pm.002$

Table 3: MSE results for different data percentage.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Domain	Frequency	Lengths	Dim	Split	Description
ETTh1	Electricity	1 hour	14,400	7	6:2:2	Power transformer 1, comprising seven indicators such as oil temperature and useful load
ETTh2	Electricity	1 hour	14,400	7	6:2:2	Power transformer 2, comprising seven indicators such as oil temperature and useful load
ETTm1	Electricity	15 mins	57,600	7	6:2:2	Power transformer 1, comprising seven indicators such as oil temperature and useful load
ETTm2	Electricity	15 mins	57,600	7	6:2:2	Power transformer 2, comprising seven indicators such as oil temperature and useful load
Weather	Environment	10 mins	52,696	21	7:1:2	Recorded every for the whole year 2020, which contains 21 meteorological indicators
Electricity	Electricity	1 hour	26,304	321	7:1:2	Electricity records the electricity consumption in kWh every 1 hour from 2012 to 2014

Appendix

Table 4: Statistics of datasets.

Models	Descriptions
Moment ( Goswami et al., 2024 )	Moment is a transformer system pre-trained on a masked time series task. It reconstructs masked portions of time series for tasks like forecasting, classification, anomaly detection, and imputation.
TTM ( Ekambaram et al., 2024b )	It is based on MLP-Mixer blocks with gated attention and multi-resolution sampling. It captures temporal patterns and cross-channel correlations for time-series forecasting, optimized for zero/few-shot learning with low computational cost.
Timer ( Liu et al., 2024e )	Timer is a GPT-style autoregressive model for time series analysis, predicting the next token in single-series sequences. It supports tasks like forecasting, imputation, and anomaly detection across different time series.
CALF ( Liu et al., 2025 )	CALF is a cross-modal knowledge distillation framework that aligns time series data with pre-trained LLMs by leveraging both static and dynamic knowledge, achieving state-of-the-art performance in both long- and short-term forecasting tasks with strong generalization abilities.
GPT4TS ( Zhou et al., 2023 )	GPT4TS fine-tunes the limited parameters of LLM, which demonstrates competitive performance by transferring knowledge from large-scale pre-training text data.
UniTime ( Liu et al., 2024b )	UniTime designs domain instructions to align time series and text modalities.

Appendix

Table 5: Descriptions of time series forecasting models in experiment.

Model		GPT4TS (2023)				CALF (2025)				UniTime (2024)
Plugin		✗		✓		✗		✓		✗		✓
Metric		MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETTh1	96	0.439	0.447	0.427	0.435	0.407	0.427	0.396	0.417	0.718	0.575	0.690	0.557
	192	0.461	0.458	0.449	0.448	0.429	0.443	0.420	0.433	0.750	0.592	0.723	0.573
	336	0.464	0.468	0.451	0.458	0.443	0.456	0.433	0.446	0.723	0.592	0.702	0.582
	720	0.509	0.512	0.497	0.496	0.495	0.495	0.487	0.484	0.767	0.623	0.739	0.606

Appendix

Table 6: The table reports MSE and MAE of LLM-based models for different forecasting horizons

F\in\{96,192,336,720\}

. The better results are highlighted in bold .

Model		Timer (2024)				Moment (2024)				TTM (2024)
CoRA		✗		✓		✗		✓		✗		✓
Metric		MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETTh1	96	0.395	0.409	0.390	0.405	0.409	0.422	0.395	0.411	0.364	0.392	0.357	0.386
	192	0.458	0.458	0.453	0.446	0.428	0.436	0.416	0.432	0.391	0.410	0.381	0.400
	336	0.496	0.487	0.495	0.479	0.457	0.451	0.449	0.441	0.411	0.430	0.408	0.426
	720	0.851	0.652	0.833	0.650	0.483	0.483	0.467	0.473	0.454	0.472	0.444	0.467

Appendix

Table 7: The table reports MSE and MAE of pre-trained models for different forecasting horizons

F\in\{96,192,336,720\}

. The better results are highlighted in bold .

Dataset	ETTm2					Electricity
Rate	5%	10%	15%	20%	25%	5%	10%	15%	20%	25%
TTM	0.164	0.162	0.163	0.160	0.157	0.146	0.143	0.145	0.141	0.142
+ LIFT	0.162	0.163	0.161	0.158	0.156	0.149	0.145	0.144	0.139	0.139
+ C-LoRA	0.166	0.163	0.162	0.159	0.155	0.148	0.146	0.147	0.140	0.141
+ CoRA	0.160 $\scriptstyle\pm 0.003$	0.158 $\scriptstyle\pm 0.002$	0.159 $\scriptstyle\pm 0.003$	0.157 $\scriptstyle\pm 0.001$	0.153 $\scriptstyle\pm 0.002$	0.143 $\scriptstyle\pm 0.003$	0.141 $\scriptstyle\pm 0.003$	0.142 $\scriptstyle\pm 0.002$	0.138 $\scriptstyle\pm 0.002$	0.135 $\scriptstyle\pm 0.001$

Appendix

Table 8: The sampling rate set to {5%, 10%, 15%, 20%, 25%}. Black : the best, Underline : the 2nd best.

Panel of Figure 6 — Figure 6: Parameter sensitivity of main hyper-parameters in CoRA.

Panel of Figure 7 — Figure 7: Visualization of Heterogeneous Spaces

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