Revisiting Identity and Spectra Dispersion in Media-Bridged Time Series Forecasting: Linking Multivariate Signals and Narrative Flows

Jierui Lei; Wenjian Zhang; Qingyi Yang; Yuyang Hong; Fangzheng Chen; Zhengbo Zhang; Haina Tang; Shiming Xiang

cs.CVOct 8, 2026

Revisiting Identity and Spectra Dispersion in Media-Bridged Time Series Forecasting: Linking Multivariate Signals and Narrative Flows

Authors: Jierui Lei, Wenjian Zhang, Qingyi Yang, Yuyang Hong, Fangzheng Chen, Zhengbo Zhang, Haina Tang, Shiming Xiang

Organizations: School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China · State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China · School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen, Guangdong 518107, China · School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China · School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049, China · College of Computer Science, Chongqing University, Chongqing 401331, China

Abstract

Media-bridged time series forecasting is expanding to encompass traditional "multivariate" and emerging "multimodal" (e.g., through textual assistance). Existing Time Series Forecasting (TSF) models still rely on paradigm-specific relation, fusion, and temporal modules, hindering a common forecasting backbone across numerical and pre-aligned narrative-flow settings. To explore this, we propose the Multimedia Identity-Aware Prism Network (MIDAPN), a unified spatiotemporal forecasting backbone based on media-general graph adaptation and automatic temporal learning: (1) Following media pre-alignment, our Multimedia Identity-Aware Graph (MIDAG) revisits identity through static essence, dynamic behavior, and latent commonality, inducing affinities that extend variable-specific dependencies across media. Contextual Identity Modulation (CIM) further refines discriminative aggregation. (2) We develop Spectral Prism Convolution (SPConv) to automatically perform hierarchical temporal analysis, balancing coarse trends and fine-grained details. Meanwhile, its Adaptive Search Guidance configures a scale-efficient architecture for temporal-dimension reconstruction. These decoupled yet synergistic components jointly address media identity disentanglement and temporal-scale mismatch. Comprehensive evaluations involving 16 SOTA TSF models across 13 "multivariate" and 12 "multimodal" datasets, alongside targeted long-context comparisons against 14 time series foundation models and fused pretrained language models, demonstrate MIDAPN's consistent superiority and broad shared backbone compatibility. The code is available at https://github.com/MIDAPN.

Figures & tables

Fig. 1: Motivations from identity awareness and temporal capturing (spatiotemporal learning). MIDAPN achieves cross-media compatibility across multivariate and multimodal forecasting, while controlled replacements of MIDAG or SPConv with generic counterparts consistently increase errors

Method	Year	External Paired Modality	Pretrained PLM/TSFM	Explicit Cross- Variate Relation	Intermediate Cross- Modal Interaction	Identity/Group-Aware Relation Modeling	Frequency-Domain Modeling	Explicit Multi-Resolution Temporal Modeling	Search-Guided Hierarchical Reconstruction
Native multivariate models and their TaTS-based extensions
MSGNet [ 17 ]	2024	✗	✗	✓	✗	✗	✓	✓	✗
+ TaTS [ 15 ]	2026	✓	✓	✓	✓	✗	✓	✓	✗
TimeFilter [ 29 ]	2025	✗	✗	✓	✗	✗	✗	✗	✗
+ TaTS [ 15 ]	2026	✓	✓	✓	✓	✗	✗	✗	✗
DUET [ 16 ]	2025	✗	✗	✓	✗	✓	✓	✗	✗

TABLE I: Comparison with representative multivariate and multimodal models.“+TaTS” denotes its TaTS-based multimodal extension.

Fig. 2: MIDAPN architecture. (a) Workflow for "multivariate" scenarios. (b) Workflow for TaTS-style "multimodal" scenarios. In both settings, TSEM-his first extracts spatiotemporal representations through Decoupled Frequency Fusion, Multimedia Identity-Aware Graph, and Spectral Prism Convolution from historical windows, then a channel-independent MLP maps the history to the future, followed by TSEM-pred for forecast refinement (details in Sec. IV-E )

Fig. 3: Core TSEM modules: (a) Decoupled Frequency Fusion (DFF); (b) Multimedia Identity-Aware Graph (MIDAG); and (c) Spectral Prism Convolution (SPConv), whose architecture is configured by Adaptive Search Guidance (ASGM). Here, $C$ and $T$ denote the numbers of aligned variates and temporal steps, respectively. MIDAPN learns multivariate dependencies and multimodal heterogeneity within a unified backbone for Spatiotemporal decoupling

Fig. 4: Normalized SVD-energy entropy of CIM refinement ( $C\times T$ ); Lower entropy values indicate stronger spectral mode concentration.

Dataset	Horizon	Max-Sum		Random		Min-Sum
Dataset	Horizon	MSE	MAE	MSE	MAE	MSE	MAE
Flight	96	0.144	0.248	0.145	0.249	0.144	0.248
Weather	96	0.147	0.188	0.145	0.186	0.145	0.185
ETTm2	96	0.171	0.252	0.172	0.253	0.168	0.249
Flight	720	0.197	0.294	0.196	0.292	0.193	0.290
ETTm2	720	0.396	0.396	0.394	0.393	0.393	0.391

TABLE II: Forecasting comparison of different expansion-factor strategies. The best results are highlighted in bold .

Fig. 5: "Adaptive Search-Guided" SPConv configuration (Left: multi-scale distributions; Right: $d_{\mathrm{ce}}$ search, cost evolution, and selected low-cost solutions), illustrating scale progression and compact architecture configuration

Datasets	Variates	RevIN	PRReg	Timestamps	Frequency
ETTm2	7	$\boldsymbol{\times}$	$\boldsymbol{\checkmark}$	69680	15mins
ETTh2	7	$\boldsymbol{\times}$	$\boldsymbol{\checkmark}$	17420	1h
Flight	7	$\boldsymbol{\checkmark}$	$\boldsymbol{\times}$	26304	1h
Weather	21	$\boldsymbol{\checkmark}$	$\boldsymbol{\times}$	52696	10mins
Traffic	862	$\boldsymbol{\checkmark}$	$\boldsymbol{\times}$	17544	1h
Electricity	321	$\boldsymbol{\checkmark}$	$\boldsymbol{\times}$	26304	1h

TABLE III: Statistics of Datasets and the Actual Use of RevIN/PRReg for MIDAPN. All time series are standardized

Models	MIDAPN		TimeFilter		VPNet		CPiRi		SEMixer		DUET		TimeKAN		FilterTS		TimePro		P-sLSTM		ModernTCN		TimeMixer		iTransformer		Time-LLM		MSGNet		PatchTST		TimesNet
(Years)	(Ours)		(ICML’25)		(ICLR’26)		(ICLR’26)		(WWW’26)		(KDD’25)		(ICLR’25)		(AAAI’25)		(ICML’25)		(AAAI’25)		(ICLR’24)		(ICLR’24)		(ICLR’24)		(ICLR’24)		(AAAI’24)		(ICLR’23)		(ICLR’23)
Metric	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETT (Avg)	0.318	0.353	0.318	0.359	0.334	0.365	0.332	0.367	0.318	0.363	0.326	0.361	0.330	0.364	0.324	0.359	0.329	0.365	0.336	0.371	0.329	0.361	0.329	0.365	0.336	0.369	0.332	0.366	0.342	0.373	0.334	0.366	0.352	0.380
Flight	0.161	0.262	0.161	0.268	0.161	0.269	0.160	0.268	0.160	0.267	0.163	0.271	0.179	0.289	0.165	0.269	0.164	0.272	0.171	0.281	0.172	0.282	0.172	0.274	0.180	0.292	0.179	0.291	0.208	0.321	0.163	0.275	0.191	0.304
Weather	0.235	0.259	0.239	0.269	0.246	0.275	0.253	0.276	0.256	0.281	0.251	0.273	0.243	0.272	0.244	0.274	0.251	0.276	0.261	0.283	0.245	0.273	0.245	0.275	0.258	0.278	0.263	0.284	0.249	0.278	0.259	0.281	0.259	0.287
Traffic	0.461	0.276	0.409	0.269	0.448	0.291	0.450	0.306	0.505	0.324	0.451	0.269	0.601	0.363	0.471	0.315	0.440	0.286	0.453	0.286	0.490	0.326	0.484	0.297	0.428	0.282	0.541	0.358	0.660	0.381	0.481	0.304	0.620	0.336

TABLE IV: Averaged Comparison across 25 “multivariate” and “multimodal” datasets in multiple future horizons. Red indicates best, while blue indicates second. Prefixes: [MV] Multivariate, [MM] Multimodal. For fairness: (1) In multivariate, 96 predict {12, 24, 48, 96} length for PEMS, 36 predict {24, 36, 48, 60} length for ILI and NASDAQ, other datasets use 96 predict {96, 192, 336, 720} in long-terms. (2) In multimodal, we use 8 predict {8, 10, 12} length for unified-granularity evaluation within TaTS [ 15 ]

Fig. 6: TSFMs, fused-PLMs and multimodal frameworks comparison (sorted by averaged MAE from low to high). MIDAPN consistently achieves the lowest MAE across the selected benchmarks, highlighting its accuracy advantage over pretrained forecasting approaches under extended look-back settings

Fig. 7: Forecasting across media-bridged domains with periodic, volatile, and trend-dominated patterns. MIDAPN generally tracks major trends and recurring oscillations, with localized deviations around abrupt changes

Task Types	Multivariate				Multimodal				Multivariate + Text
Datasets	Electricity		Weather		Traffic		Energy		LEU
Strategies	Avg	Drop	Avg	Drop	Avg	Drop	Avg	Drop	Avg	Drop
MIDAPN	0.2135	—	0.2468	—	0.1963	—	0.2478	—	0.5665	—
w/o DFF	0.2389	11.89%	0.2541	2.99%	0.2122	8.06%	0.2560	3.30%	0.6233	10.03%
w/o MIDAG	0.2384	11.65%	0.2526	2.38%	0.2113	7.64%	0.2555	3.09%	0.7015	23.83%
w/o SPConv	0.2428	13.70%	0.2546	3.19%	0.2117	7.81%	0.2508	1.21%	0.5792	2.24%

TABLE V: Ablation studies (For averaged horizons, multivariate: {96, 192, 336, 720}, multimodal: {8, 10, 12}). The "Drop" is the error percentage increase in Average of MAE and MSE

Fig. 8: Identity-Aware Graph Adaptation (multivariate: Traffic, multimodal: Climate, multivariate + text: MSPG). (a, b, c): Variate identity visualizations; (d): Clustering visualization; (e): Cross-level Affinity Decomposition

Fig. 9: “Narrative-Flow” forecasting on the Agriculture dataset across declining, uncertain, and rising narrative-guided market periods

Task Types	Multivariate				Multimodal				Multivariate + Text
Datasets	Solar		Weather		Climate		Agriculture		PTF
Backbone & Models	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE
SageFormer [ 24 ]	0.259	0.197	0.206	0.162	0.766	0.912	0.242	0.136	0.595	0.674
(Transformer)+MIDAG	0.235	0.189	0.198	0.161	0.762	0.909	0.240	0.131	0.548	0.635
DLinear [ 56 ]	0.236	0.312	0.255	0.196	0.765	0.920	0.304	0.194	0.953	1.454
(Linear)+MIDAG	0.229	0.190	0.218	0.164	0.748	0.902	0.286	0.152	0.568	0.628

TABLE VI: MIDAG Generalization in "multivariate" (input-96-predict-96) and "multimodal" (input-8-predict-12) scenarios

Fig. 10: Hyperparameter analysis. (a): Sensitivity analysis (PEMS04, Input-96-predict-12); (b): Optimal Selection (Multimodal, Input-8-predict-12)

Fig. 11: Text encoder evaluation. (a): Easily predictable domains; (b): Challenging domains. (Embedding dimension: [BERT:768, BERT-XL:1024, GPT2:768, GPT2-XL:1600, LLaMA3.2-1B:2048, LLaMA2-7B/LLaMA3-8B:4096, Qwen3-0.6B:1024, Qwen2/Deepseek-distil-1.5B:1536, Qwen3-8B:4096], Input-8-predict-12). The contribution of PLMs remains inconclusive

Fig. 12: Performance, efficiency and memory footprint comparison. (a): Input-96-predict-720 for Electricity; (b): Input-8-predict-12 for Health. By selectively ablating $\text{TSEM}_{\text{his}}$ and $\text{TSEM}_{\text{pred}}$ , MIDAPN can achieve the most expeditious training speed compared to other SOTA TSF models

Datasets	Variates	RevIN	PRReg	Timestamps	Frequency	Properties	Date
ETTm2	7	$\boldsymbol{\times}$	$\boldsymbol{\checkmark}$	69680	15mins	Volatility & Periodicity	2016.7.1-2018.6.26
ETTh2	7	$\boldsymbol{\times}$	$\boldsymbol{\checkmark}$	17420	1h	Volatility & Periodicity	2016.7.1-2018.6.26
Flight	7	$\boldsymbol{\checkmark}$	$\boldsymbol{\times}$	26304	1h	Volatility	2019.1.1-2021.12.31
Weather	21	$\boldsymbol{\checkmark}$	$\boldsymbol{\times}$	52696	10mins	Fluctuation	2020.1.1-2021.1.1
Traffic	862	$\boldsymbol{\checkmark}$	$\boldsymbol{\times}$	17544	1h	Stable Periodicity	2016.7.1-2018.7.2
Electricity	321	$\boldsymbol{\checkmark}$	$\boldsymbol{\times}$	26304	1h	Stable Periodicity	2016.7.1-2019.7.2

TABLE VII: Statistics of Datasets and the Actual Use of RevIN/PRReg for MIDAPN

	MIDAPN -nonloss		MIDAPN -loss-0.001		MIDAPN -loss-0.01
Dataset	MSE	MAE	MSE	MAE	MSE	MAE
Agriculture	0.1314	0.2317	0.1315	0.2320	0.1323	0.2334
Climate	0.9061	0.7618	0.9059	0.7617	0.9116	0.7638
Energy	0.1834	0.3359	0.1968	0.3436	0.1877	0.3407
Environment	0.2691	0.3677	0.2694	0.3719	0.2691	0.3682
Health	0.8322	0.6260	0.8365	0.6287	0.8716	0.6423

TABLE VIII: Performance comparison with the auxiliary assignment. Red / Blue indicate 1st / 2nd

Dataset	Model	MSE	MAE
Multivariate datasets
ETTh2	MIDAPN	$0.368\pm 0.003$	$0.392\pm 0.002$
ETTm2	MIDAPN	$0.271\pm 0.001$	$0.316\pm 0.001$
Flight	MIDAPN	$0.161\pm 0.000$	$0.262\pm 0.000$
Weather	MIDAPN	$0.236\pm 0.001$	$0.260\pm 0.001$
PEMS03	MIDAPN	$0.096\pm 0.001$	$0.201\pm 0.001$

TABLE IX: Forecasting results over five random seeds

Dataset	Metric	Text-Embedding Dimension
Dataset	Metric	4	8	12	24	48	96
Climate	MSE	0.910	0.910	0.890	0.905	0.906	0.907
Climate	MAE	0.766	0.765	0.757	0.763	0.763	0.764
Energy	MSE	0.182	0.176	0.172	0.178	0.178	0.177
Energy	MAE	0.330	0.327	0.324	0.327	0.328	0.327
Environment	MSE	0.269	0.268	0.267	0.268	0.270	0.270

TABLE X: Performance under different textual dimensions

Models		MIDAPN		TimeFilter		VPNet		CPiRi		SEMixer		DUET		TimeKAN		FilterTS		TimePro		P_sLSTM		ModernTCN		TimeMixer		iTransformer		TimeLLM		MGSNET		PatchTST		TimesNet
(Years)		(Ours)		(2025)		(2026)		(2026)		(2026)		(2025)		(2025)		(2025)		(2025)		(2025)		(2024)		(2024)		(2024)		(2024)		(2024)		(2023)		(2023)
Metric		MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETTm2	96	0.168	0.250	0.169	0.255	0.173	0.254	0.178	0.259	0.176	0.262	0.174	0.255	0.174	0.255	0.172	0.255	0.178	0.260	0.181	0.267	0.175	0.256	0.174	0.258	0.180	0.264	0.178	0.262	0.177	0.262	0.175	0.259	0.187	0.267
	192	0.230	0.294	0.235	0.299	0.247	0.305	0.245	0.305	0.243	0.310	0.243	0.302	0.239	0.299	0.237	0.299	0.242	0.303	0.250	0.312	0.239	0.298	0.239	0.302	0.250	0.309	0.243	0.304	0.247	0.307	0.241	0.302	0.249	0.309
	336	0.295	0.330	0.293	0.336	0.322	0.349	0.306	0.344	0.306	0.351	0.304	0.341	0.301	0.340	0.299	0.398	0.303	0.342	0.315	0.353	0.298	0.336	0.296	0.340	0.311	0.348	0.308	0.345	0.312	0.346	0.305	0.343	0.321	0.351
	720	0.391	0.389	0.390	0.393	0.430	0.412	0.403	0.401	0.407	0.416	0.399	0.397	0.395	0.396	0.397	0.394	0.400	0.399	0.418	0.413	0.401	0.395	0.393	0.397	0.412	0.407	0.408	0.407	0.414	0.403	0.402	0.400	0.408	0.403

TABLE XI: Comprehensive performance comparison in long-term forecasting. Results are highlighted strictly following the Dense Ranking principle. Red / Blue indicate 1st / 2nd

Models		MIDAPN		TimeFilter		VPNet		CPiRi		SEMixer		DUET		TimeKAN		FilterTS		TimePro		P_sLSTM		ModernTCN		TimeMixer		iTransformer		TimeLLM		MGSNET		PatchTST		TimesNet
(Years)		(Ours)		(2025)		(2026)		(2026)		(2026)		(2025)		(2025)		(2025)		(2025)		(2025)		(2024)		(2024)		(2024)		(2024)		(2024)		(2023)		(2023)
Metric		MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
Pems03	12	0.060	0.161	0.067	0.169	0.066	0.170	0.077	0.190	0.081	0.191	0.064	0.166	0.093	0.206	0.094	0.202	0.076	0.180	0.077	0.183	0.069	0.174	0.076	0.188	0.071	0.174	0.095	0.208	0.078	0.187	0.099	0.216	0.085	0.192
	24	0.076	0.181	0.085	0.192	0.090	0.201	0.097	0.213	0.122	0.236	0.081	0.186	0.155	0.269	0.112	0.222	0.101	0.210	0.109	0.219	0.093	0.203	0.113	0.226	0.093	0.201	0.135	0.248	0.108	0.218	0.142	0.259	0.118	0.223
	48	0.103	0.211	0.126	0.236	0.138	0.252	0.140	0.253	0.195	0.302	0.114	0.222	0.236	0.337	0.160	0.265	0.137	0.248	0.163	0.270	0.141	0.250	0.191	0.292	0.125	0.236	0.198	0.302	0.178	0.272	0.211	0.319	0.155	0.260
	96	0.143	0.248	0.173	0.283	0.201	0.311	0.174	0.289	0.255	0.354	0.175	0.283	0.306	0.399	0.208	0.307	0.184	0.292	0.209	0.309	0.208	0.306	0.288	0.363	0.164	0.275	0.243	0.342	0.238	0.328	0.269	0.370	0.228	0.317

TABLE XII: Comprehensive performance comparison in short-term forecasting. Results are highlighted strictly following the Dense Ranking principle. Red / Blue indicate 1st / 2nd

Models		MIDAPN		TimeFilter		VPNet		CPiRi		SEMixer		DUET		TimeKAN		FilterTS		TimePro		P_sLSTM		ModernTCN		TimeMixer		iTransformer		TimeLLM		MGSNET		PatchTST		TimesNet
(Years)		(Ours)		(2025)		(2026)		(2026)		(2026)		(2025)		(2025)		(2025)		(2025)		(2025)		(2024)		(2024)		(2024)		(2024)		(2024)		(2023)		(2023)
Metric		MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
Agriculture	8	0.080	0.182	0.083	0.191	0.082	0.188	0.079	0.182	0.083	0.189	0.099	0.220	0.107	0.220	0.082	0.185	0.082	0.195	0.084	0.187	0.080	0.180	0.107	0.221	0.078	0.187	0.081	0.187	0.084	0.194	0.080	0.188	0.086	0.202
	10	0.102	0.207	0.105	0.213	0.103	0.211	0.102	0.210	0.103	0.211	0.105	0.221	0.124	0.238	0.105	0.210	0.105	0.216	0.109	0.214	0.103	0.208	0.121	0.234	0.101	0.210	0.106	0.214	0.112	0.229	0.104	0.214	0.104	0.216
	12	0.131	0.232	0.134	0.237	0.131	0.236	0.135	0.244	0.134	0.236	0.134	0.239	0.154	0.261	0.133	0.238	0.133	0.241	0.137	0.238	0.136	0.234	0.149	0.262	0.132	0.235	0.137	0.240	0.141	0.248	0.133	0.240	0.136	0.248
	Average	0.104	0.207	0.107	0.214	0.105	0.212	0.105	0.212	0.107	0.212	0.113	0.227	0.128	0.240	0.107	0.211	0.107	0.217	0.110	0.213	0.106	0.207	0.126	0.239	0.104	0.211	0.108	0.214	0.112	0.224	0.106	0.214	0.109	0.222

TABLE XIII: Comprehensive performance comparison across “multimodal scenarios for different prediction horizons (8, 10, 12). Results are highlighted strictly following the Dense Ranking principle. Red / Blue indicate 1st / 2nd

Models		MIDAPN		GTM		SE-LLM		CORA		Aurora		DualSG		Time-VLM		SEMPO		Sundial		CALF		MOIRAI
(Years)		(Ours)		(2026)		(2026)		(2026)		(2026)		(2025)		(2025)		(2025)		(2025)		(2025)		(2024)
Metric		MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
Weather	96	0.140	0.179	0.147	0.197	0.150	0.200	0.149	0.194	0.160	0.207	0.156	0.201	0.148	0.200	0.154	0.205	0.157	0.205	0.160	0.208	0.199	0.211
	192	0.190	0.228	0.192	0.241	0.194	0.243	0.193	0.237	0.202	0.247	0.196	0.239	0.193	0.240	0.198	0.246	0.205	0.251	0.205	0.252	0.246	0.251
	336	0.245	0.275	0.250	0.291	0.247	0.285	0.240	0.274	0.252	0.288	0.248	0.280	0.243	0.281	0.249	0.285	0.253	0.289	0.253	0.288	0.274	0.291
	720	0.316	0.328	0.310	0.334	0.323	0.339	0.313	0.322	0.307	0.327	0.323	0.334	0.312	0.332	0.321	0.337	0.320	0.336	0.329	0.341	0.337	0.340

TABLE XIV: Comprehensive performance comparison on Weather and Electricity datasets for different prediction horizons (96, 192, 336, 720). Results are highlighted strictly following the Dense Ranking principle. Red / Blue indicate 1st / 2nd

Models		MIDAPN		Aurora		SE-LLM		VoT		Time-VLM		CALF		ChatTime		GPT4MTS		MM-TSFLib
(Years)		(Ours)		(2026)		(2026)		(2026)		(2025)		(2025)		(2025)		(2024)		(2024)
Metric		MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
Traffic	8	0.157	0.224	0.158	0.286	0.172	0.229	0.167	0.231	0.212	0.313	0.176	0.232	0.257	0.347	0.195	0.256	0.195	0.250
	12	0.176	0.236	0.168	0.294	0.191	0.232	0.181	0.239	0.222	0.322	0.193	0.243	0.261	0.349	0.218	0.268	0.261	0.272
	Average	0.167	0.230	0.163	0.290	0.182	0.231	0.174	0.235	0.217	0.318	0.185	0.238	0.259	0.348	0.207	0.262	0.228	0.261
Health	24	0.958	0.648	1.332	0.796	1.232	0.774	1.210	0.707	1.491	0.839	1.451	0.749	1.758	0.888	1.513	0.802	1.562	0.768

TABLE XV: Performance comparison on Traffic, Health, and Environment datasets. Results are highlighted strictly following the Dense Ranking principle. Red / Blue indicate 1st / 2nd

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