The Future Is Finer: Multivariate Time Series Super-Resolution Forecasting
Authors: Shuhao Li, Weidong Yang, Yue Cui, Fan Zhang, Lu Qin
Organizations: Fudan University, Shanghai, China · Nanyang Technological University, Singapore · Zhuhai Fudan Innovation Research Institute, Zhuhai, China · Tongyi Laboratory, Alibaba Group, Hangzhou, China · Guangzhou University, Guangzhou, China · University of Technology Sydney, Sydney, Australia
Web platforms run on multivariate time series, from service telemetry and Web traffic logs to sensor streams served through Web APIs. Yet, retention policies often archive them at coarse granularity to save storage and bandwidth. Decisions such as autoscaling, alerting, and billing operate at finer granularity than existing forecasters reach, since these models predict at the resolution of their input. We therefore introduce Multivariate Time Series Super-Resolution Forecasting (MTS-SRF), which forecasts fine-grained futures from coarse histories, and propose TimeMagnifier to address its three challenges. Fourier Anchor counters data sparsity by fitting each input window to a trend-Fourier structure with sparse cross-variable gating; De-noise Only constrains fine-grained ambiguity by refining along the resolution axis rather than the noise axis, lengthening the grid level by level; and banded DTW Alignment corrects cross-resolution misalignment against the coarse forecast. On the first MTS-SRF benchmark, with ten datasets from five domains, real archived cross-resolution pairs, strengthened baseline adaptations, and five-seed significance tests, TimeMagnifier is best on every dataset, resolution coefficient, and metric against 15 baselines and cuts MSE by 12.3% on average. Its De-noise Only and DTW stages also transfer as a plug-in that lowers the MSE of existing forecasters by 5.1% to 9.0%. Code will be made publicly available.
Figures & tables
Figure 1. Same-resolution forecasting versus MTS-SRF from the same hourly history. The hourly forecast returns only on-hour values, while the 10-minute forecast recovers the wind crest between them that crosses the alert level.
Figure 2. An example of the multivariate time series super-resolution forecasting problem, where the low-resolution coefficient is Γ=4 , i.e., ΔτG=4Δτmin , and the high-resolution coefficient is γ=2 , i.e., Δτg=2Δτmin .
Figure 3. Illustration of TimeMagnifier’s architectural framework and inference data flow with Γ=4,γ=2 as an example.
Category
Models
Metrics
BJAir
ETTh1
ETTh2
ETTm1
ETTm2
Electricity
ExRate
Illness
Traffic
Weather
Γ=2
Γ=4
Γ=2
Γ=4
Γ=2
Γ=4
Γ=2
Γ=4
Γ=2
Γ=4
Γ=2
Γ=4
Γ=2
Γ=4
Γ=2
Γ=4
Γ=2
Γ=4
Γ=2
Γ=4
Transformer-based
Transformer
MSE
0.9431
1.0685
1.1564
1.1454
1.7930
1.9874
1.6275
1.6526
1.1175
1.2153
0.4665
0.4923
1.2372
1.3889
4.3217
4.6351
1.1573
1.3446
1.1214
1.1643
MAE
0.7321
0.7888
0.9540
0.9808
1.1406
1.2586
1.2037
1.2204
0.9581
1.0350
0.6187
0.6604
0.9673
1.0488
1.7474
1.7802
0.6423
0.7376
0.8519
0.9214
Informer
MSE
1.0782
1.2093
1.1967
1.2143
1.9497
2.0843
1.6675
1.6983
1.2605
1.3879
0.5653
0.6526
1.3198
1.3937
4.5686
4.7428
1.5136
1.8341
1.1657
1.2052
MAE
0.7809
0.8269
0.9845
1.0378
1.1533
1.1882
1.1673
1.1773
0.9513
1.0995
0.6892
0.7548
0.8784
0.8955
1.6226
1.6495
0.8202
0.9478
0.8914
0.9503
Autoformer
MSE
0.8644
0.9352
0.6564
0.7307
0.8208
0.9106
0.8470
0.8552
0.5438
0.8276
0.4091
0.5110
0.9909
1.2998
3.6372
3.9121
1.0796
1.3081
0.5776
0.5855
Table 1. Main results. The brown background marks the best result and the gray background the second best.
Adapter
ETTh1
Weather
TQNet
iTrans.
TQNet
iTrans.
P0 linear head (Table 1 )
0.6946
0.7151
0.3831
0.4029
P1 fine-grid head
0.7038
0.7165
0.3880
0.4088
P2 forecast, then spline
0.7330
0.7353
0.4041
0.4173
P3 spline, then forecast
0.7190
0.7308
0.3916
0.4166
P4 sub-pixel upsampler
0.6935
0.7152
0.3889
0.4053
Table 2. MSE of baseline adapters at Γ=4 ; P1 to P4 use the same splits and 20-trial budget as TimeMagnifier.
Figure 4. Look-back study at Γ=2 and horizon 336. MSE is shaded by its gap to each dataset’s best window (bold). ∗ Illness uses horizon 36 and windows 12, 18, 24, 36 and 48.
Horizon
BJAir
ETTh1
ETTh2
ETTm1
ETTm2
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
96
0.5144
0.4372
0.4341
0.4504
0.4661
0.4709
0.3519
0.3754
0.2202
0.3123
192
0.5822
0.4707
0.4914
0.4850
0.5363
0.4906
0.3919
0.4197
0.3607
0.4100
336
0.6949
0.5222
0.5865
0.5380
0.7859
0.5044
0.4811
0.4706
0.4855
0.5237
729
0.8882
0.6437
0.7496
0.6633
0.8469
0.5143
0.5560
0.5343
0.6132
0.6288
Horizon
Electricity
ExRate
Illness
Traffic
Weather
Table 3. Results across different forecast horizons.
Models
Metrics
ETTh1
Electricity
Traffic
Γ=2
Γ=4
Γ=2
Γ=4
Γ=2
Γ=4
DLinear
MSE
0.6426
0.7273
0.3015
0.3783
0.7835
0.9885
MAE
0.6373
0.7198
0.4735
0.5518
0.5394
0.6395
PatchTST
MSE
0.6598
0.7039
0.2943
0.3099
0.6242
0.7307
MAE
0.6436
0.7138
0.4610
0.4848
0.4396
0.5119
DLinear
MSE
0.5988
0.6619
0.2849
0.3589
0.7393
0.9054
Table 4. Comparison of baseline linear adaptation and De-noise Only & DTW plug-in adaptation for the MTS-SRF task.
Figure 5. Ablation study results. Longer lines indicate greater degradation in predictive accuracy.
Figure 6. Resolution study: Γ with γ=1 (a, b) and γ with Γ=6 (c, d); Γ=1 and γ=6 are same-resolution controls.
Datasets
Timestamps
Channels
Freq.( Δτmin )
Domain
BJAir
36,000
9
1 hour
Environment
ETTh1
14,400
7
1 hour
Energy
ETTh2
14,400
7
1 hour
Energy
ETTm1
57,600
7
15 min
Energy
ETTm2
57,600
7
15 min
Energy
Electricity
26,304
321
1 hour
Energy
Table 5. Dataset statistics.
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
Dataset
TimeMagnifier
Runner-up in Table 1
p
ETTh2
0.781 ± 0.008
TQNet
0.799 ± 0.009
0.0015
BJAir
0.690 ± 0.006
iTransformer
0.717 ± 0.011
0.0021
ExRate
0.950 ± 0.019
TimeMixer
0.980 ± 0.017
0.0027
Illness
2.806 ± 0.149
NLinear
2.922 ± 0.154
0.255
Appendix
Table 6. Smallest-gap cells over five seeds ( Γ=2 , MSE).
Band
TM ρ
TM C
TQNet ρ
TQNet C
below 0.5fN
0.95
0.79
1.05
0.54
0.5fN to fN
0.91
0.69
1.31
0.45
above fN
0.81
0.16
1.12
0.08
Appendix
Table 7. Band-wise power ratio ρ and coherence C on ETTm1 ( Γ=4 ).
Alignment
ETTh1
Traffic
Time (Traffic)
None
0.7157
0.7953
0.81
Banded DTW, Euclidean
0.6965
0.7257
1.03
Shared path, cosine
0.6701
0.7604
0.95
Soft-DTW, same band
0.6761
0.7139
2.22
Ours
0.5933
0.6729
1.00
Appendix
Table 8. Alignment alternatives ( Γ=4 ; MSE, time ratio).
Figure 7. Training time per iteration and MSE on Electricity at Γ=2 , with bubble area proportional to trainable parameters; all models use the same GPU and batch size.
Time series forecasting is vital across many domains, yet existing models struggle with fixed-length inputs and inadequate multi-scale modeling. We propose MR-CDM, a framework combining hierarchical multi-resolution trend decomposition, an adaptive embedding mechanism for variable-length inputs, and a multi-scale conditional diffusion process. Evaluations on four real-world datasets demonstrate that MR-CDM significantly outperforms state-of-the-art baselines (e.g., CSDI, Informer), reducing MAE and RMSE by approximately 6-10 to a certain degree.
Xianyong Xu, Yuanjun Zuo, Zhihong Huang +4
Department, State Grid Hunan Electric Power Company Limited Research Institute & Hunan Province Engineering Technology Research Center of Electric Power Multimodal Perception and Edge Intelligence, Changsha, Hunan, China. · College of Computer Science, Hunan University, Changsha, Hunan, China.
Fine-grained time series data with high temporal resolution is critical for accurate analytics across a wide range of applications. However, the acquisition of such data is often limited by cost and feasibility. This problem can be tackled by reconstructing high-resolution signals from low-resolution inputs based on specific priors, known as super-resolution. While extensively studied in computer vision, directly transferring image super-resolution techniques to time series is not trivial. To address this challenge at a fundamental level, we propose Super-Resolution for Time series (SRT), a novel framework that reconstructs temporal patterns lost in low-resolution inputs via disentangled rectified flow. SRT decomposes the input into trend and seasonal components, aligns them to the target resolution using an implicit neural representation, and leverages a novel cross-resolution attention mechanism to guide the generation of high-resolution details. We further introduce SRT-large, a scaled-up version with extensive pre-training, which enables strong zero-shot super-resolution capability. Extensive experiments on nine public datasets demonstrate that SRT and SRT-large consistently outperform existing methods across multiple scale factors, showing both robust performance and the effectiveness of each component in our architecture.
Irregular Multivariate Time Series (IMTS) are characterized by uneven intervals between consecutive timestamps, which carry sampling pattern information valuable and informative for learning temporal and variable dependencies. In addition, IMTS often exhibit diverse dependencies across multiple time scales. However, many existing multi-scale IMTS methods use resampling to obtain the coarse series, which can alter the original timestamps and disrupt the sampling pattern information. To address the challenge, we propose ReIMTS, a Recursive multi-scale modeling approach for Irregular Multivariate Time Series forecasting. Instead of resampling, ReIMTS keeps timestamps unchanged and recursively splits each sample into subsamples with progressively shorter time periods. Based on the original sampling timestamps in these long-to-short subsamples, an irregularity-aware representation fusion mechanism is proposed to capture global-to-local dependencies for accurate forecasting. Extensive experiments demonstrate an average performance improvement of 27.1% in the forecasting task across different models and real-world datasets. Our code is available at https://github.com/Ladbaby/PyOmniTS.
Boyuan Li, Zhen Liu, Yicheng Luo +1
School of Computer Science and Engineering, South China University of Technology