The Future Is Finer: Multivariate Time Series Super-Resolution Forecasting

Shuhao Li; Weidong Yang; Yue Cui; Fan Zhang; Lu Qin

cs.AIOct 24, 2026

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 ·

Abstract

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

\Gamma=4

, i.e.,

\Delta\tau_{G}=4\Delta\tau_{\text{min}}

, and the high-resolution coefficient is

\gamma=2

, i.e.,

\Delta\tau_{g}=2\Delta\tau_{\text{min}}

Figure 3. Illustration of TimeMagnifier’s architectural framework and inference data flow with $\Gamma=4,\gamma=2$ as an example.

Category	Models	Metrics	BJAir		ETTh1		ETTh2		ETTm1		ETTm2		Electricity		ExRate		Illness		Traffic		Weather
Category	Models	Metrics	$\boldsymbol{\Gamma\!=\!2}$	$\boldsymbol{\Gamma\!=\!4}$	$\boldsymbol{\Gamma\!=\!2}$	$\boldsymbol{\Gamma\!=\!4}$	$\boldsymbol{\Gamma\!=\!2}$	$\boldsymbol{\Gamma\!=\!4}$	$\boldsymbol{\Gamma\!=\!2}$	$\boldsymbol{\Gamma\!=\!4}$	$\boldsymbol{\Gamma\!=\!2}$	$\boldsymbol{\Gamma\!=\!4}$	$\boldsymbol{\Gamma\!=\!2}$	$\boldsymbol{\Gamma\!=\!4}$	$\boldsymbol{\Gamma\!=\!2}$	$\boldsymbol{\Gamma\!=\!4}$	$\boldsymbol{\Gamma\!=\!2}$	$\boldsymbol{\Gamma\!=\!4}$	$\boldsymbol{\Gamma\!=\!2}$	$\boldsymbol{\Gamma\!=\!4}$	$\boldsymbol{\Gamma\!=\!2}$	$\boldsymbol{\Gamma\!=\!4}$
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
	Transformer	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
	Informer	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
Adapter	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

\Gamma=4

; P1 to P4 use the same splits and 20-trial budget as TimeMagnifier.

Figure 4. Look-back study at $\Gamma=2$ 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
Horizon	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
Models	Metrics	$\Gamma=2$	$\Gamma=4$	$\Gamma=2$	$\Gamma=4$	$\Gamma=2$	$\Gamma=4$
DLinear	MSE	0.6426	0.7273	0.3015	0.3783	0.7835	0.9885
DLinear	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
PatchTST	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.

Panel of Figure 5 — Figure 5. Ablation study results. Longer lines indicate greater degradation in predictive accuracy.

Panel of Figure 6 — Figure 6. Resolution study: $\Gamma$ with $\gamma=1$ (a, b) and $\gamma$ with $\Gamma=6$ (c, d); $\Gamma=1$ and $\gamma=6$ are same-resolution controls.

Datasets	Timestamps	Channels	Freq.( $\Delta\tau_{\text{min}}$ )	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 $\pm$ 0.008	TQNet	0.799 $\pm$ 0.009	0.0015
BJAir	0.690 $\pm$ 0.006	iTransformer	0.717 $\pm$ 0.011	0.0021
ExRate	0.950 $\pm$ 0.019	TimeMixer	0.980 $\pm$ 0.017	0.0027
Illness	2.806 $\pm$ 0.149	NLinear	2.922 $\pm$ 0.154	0.255

Appendix

Table 6. Smallest-gap cells over five seeds (

\Gamma=2

, MSE).

Band	TM $\rho$	TM $C$	TQNet $\rho$	TQNet $C$
below $0.5f_{N}$	0.95	0.79	1.05	0.54
$0.5f_{N}$ to $f_{N}$	0.91	0.69	1.31	0.45
above $f_{N}$	0.81	0.16	1.12	0.08

Appendix

Table 7. Band-wise power ratio

\rho

and coherence

C

on ETTm1 (

\Gamma=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 (

\Gamma=4

; MSE, time ratio).

Figure 7. Training time per iteration and MSE on Electricity at $\Gamma=2$ , with bubble area proportional to trainable parameters; all models use the same GPU and batch size.

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