Baguan-TS: A Sequence-Native In-Context Learning Model for Time Series Forecasting with Covariates

Linxiao Yang; Xue Jiang; Gezheng Xu; Tian Zhou; Min Yang; ZhaoYang Zhu; Linyuan Geng; Zhipeng Zeng

cs.LGMar 18, 2026

Baguan-TS: A Sequence-Native In-Context Learning Model for Time Series Forecasting with Covariates

Authors: Linxiao Yang, Xue Jiang, Gezheng Xu, Tian Zhou, Min Yang, ZhaoYang Zhu, Linyuan Geng, Zhipeng Zeng,

Organizations: DAMO Academy, Alibaba Group, Hangzhou, China

Abstract

Transformers enable in-context learning (ICL) for rapid, gradient-free adaptation in time series forecasting, yet most ICL-style approaches rely on tabularized, hand-crafted features, while end-to-end sequence models lack inference-time adaptation. We bridge this gap with a unified framework, Baguan-TS, which integrates the raw-sequence representation learning with ICL, instantiated by a 3D Transformer that attends jointly over temporal, variable, and context axes. To make this high-capacity model practical, we tackle two key hurdles: (i) calibration and training stability, improved with a feature-agnostic, target-space retrieval-based local calibration; and (ii) output oversmoothing, mitigated via context-overfitting strategy. On public benchmark with covariates, Baguan-TS consistently outperforms established baselines, achieving the highest win rate and significant reductions in both point and probabilistic forecasting metrics. Further evaluations across diverse real-world energy datasets demonstrate its robustness, yielding substantial improvements.

Figures & tables

Figure 1: Three paradigms for time series forecasting: (a) End-to-end sequence models learn from raw histories but lack in-context adaptation at inference. (b) Tabular ICL approaches (e.g., TabPFN) perform ICL over feature-engineered representations. (c) Our unified approach (Baguan-TS) enables sequence-native ICL on raw multivariate inputs, attending over temporal, variables, and context for gradient-free adaptation.

Figure 2: Probabilistic forecasting results on fev-bench-cov (30 covariate-aware tasks): Baguan-TS leads all baselines, achieving the highest average win rate and lowest average SQL.

Models	Raw time sequence	ICL (gradient- free)	No hand- crafted features	Cross- variable interaction	Local retrieval-based calibration
End-to-end models (PatchTST, FedFormer)	$\checkmark$	$\times$	$\checkmark$	$\times$	$\times$
Large pretrained models (Chronos, TimesFM, Tirex)	$\checkmark$	$\times$	$\checkmark$	$\times$	$\times$
Tabular ICL-style models (TabPFN-TS)	$\times$	$\checkmark$	$\times$	$\checkmark$	$\times$
Ours (Baguan-TS)	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$

Table 1: Capability comparison of representative time series forecasting approaches.

Figure 3: Overall architecture of Baguan-TS. The input tensor $\mathcal{Y}\in\mathbb{R}^{(C+1)\times(T+H)\times(M+1)}$ is encoded into patch tokens, then iteratively processed by stacked 3D Transformer blocks performing variable, temporal, and context attention, and finally mapped by a prediction head to produce the forecasting outputs $\mathbf{y}^{f}\in\mathbb{R}^{H}$ .

Panel of Figure 4 — Figure 4: Context organization strategies and t-SNE visualization. (a) Three context organization methods: (i) uniform splits ( green ); (ii) covariate-based retrieval in X-space ( purple , relies on feature engineering); (iii) target-based retrieval in Y-space (ours, yellow ), which focuses on historical patterns and is feature-agnostic. Higher similarity scores indicate stronger contextual relevance. (b) t-SNE plots of prediction horizons on epf (top) and entsoe (bottom) for three RBfcst variants. The ground truth (red star) lies closest to the Y-space RBfcst cluster (shaded), indicating it best captures the true pattern.

Panel of Figure 5 — Figure 5: Illustration of the context-overfitting strategy. (a) Original design, where the model forecasts query targets from retrieved context episodes. (b) Duplicate-context design: a short segment from one context slice is copied into a query, and the model is trained to retrieve the matching context and reconstruct its targets.

Figure 6: Effect of the context-overfitting strategy. Main: training loss curves for the baseline model (green) and our context-overfitting strategy (red). Insets: example forecasts compared with ground truth (blue). The baseline oversmooths outputs and misses high-frequency spikes (right); our strategy keeps a low loss while recovering spike patterns by matching contextual templates (left).

Model	SQL	MASE	WAPE	WQL
Chronos-Bolt	0.9190	1.1233	0.2702	0.2181
Moirai-2.0	0.9202	1.1233	0.2750	0.2226
Sundial-Base	1.0172	1.1449	0.2813	0.2498
TimesFM-2.5	0.8276	1.0122	0.2592	0.2095
TabPFN-TS	0.8404	1.0430	0.2015	0.1643
TiRex	0.8927	1.1081	0.2753	0.2233

Table 2: Average results on fev-bench-cov . The best results are highlighted in bold , and the second-best results are underlined .

Model	SQL	MASE	WAPE	WQL
Chronos-Bolt	0.5101	0.6350	0.0976	0.0783
Moirai-2.0	0.7139	0.8875	0.1031	0.0860
Sundial-Base	0.7486	0.9042	0.1133	0.0981
TabPFN-TS	0.4663	0.6115	0.0688	0.0537
TimesFM-2.0	0.8418	0.9278	0.1093	0.0954
TiRex	0.5710	0.7094	0.0975	0.0784

Table 3: Average results on real-world application datasets. The best results are highlighted in bold , and the second-best results are underlined .

Figure 7: Evaluation on fev-bench-uni (10 univariate/multivariate tasks). Baguan-TS achieves competitive probabilistic forecasting performance on tasks without covariates.

Method	entsoe_1H				hermes
Method	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL
w/o RBfcst	0.4284	0.5387	0.0328	0.0262	0.6607	0.8445	0.0032	0.0025
X-space	0.4185	0.5178	0.0313	0.0256	0.6186	0.7973	0.0030	0.0023
XY-space	0.4005	0.4972	0.0297	0.0241	0.6186	0.7972	0.0030	0.0023
Y-space	0.3859	0.4819	0.0287	0.0231	0.6185	0.7971	0.0030	0.0023

Table 4: Probabilistic and point forecasting evaluation for different RBfcst variants on entsoe_1H and hermes datasets.

Figure 8: Robustness evaluation on epf_fr under Gaussian white noise, random walk noise, and periodic noise, with

\kappa\in\{0,0.05,0.1,0.2,0.4,0.6,0.8,1.0\}

Panel of Figure 9 — Figure 9: Ablation of the context-overfitting strategy. (a) The full model (red) consistently outperforms the baseline (green) on synthetic periodic spike data for all $k$ , where larger $k$ corresponds to sharper spikes. (b) Attention map for a representative peak step (orange dotted line).

Model	SQL	MASE	WAPE	WQL
Ours (2D mode)	0.8769	1.0705	0.2333	0.1863
Ours (3D mode)	0.8333	1.0220	0.2285	0.1830
Ours (Ensemble)	0.7997	0.9857	0.2173	0.1724

Table 5: Average results on fev-bench-cov under different inference modes of Baguan-TS model.

Panel of Figure 10 — Figure 10: Residual correlation analysis of 2D and 3D inference modes. (a) Aggregated Pearson correlation across 30 tasks in fev-bench-cov . (b) Joint residual distribution for entsoe_1H , where darker blue bins indicate higher data density. Points along the red dashed identity line ( $y=x$ ) represent cases in which the errors in both modes are equal. Deviations from this diagonal, particularly in the second and fourth quadrants, highlight the complementary error structures between the two modes.

Figure 11: Calibration histograms of ground-truth quantile levels in predicted CDFs for different inference modes on entsoe_1H . A well-calibrated model yields a uniform histogram (red dashed line). The 2D mode is under-confident (peaked), the 3D mode is over-confident (U-shaped), whereas the ensemble effectively cancels these biases and approaches the ideal uniform distribution.

Appendix figures & tables28 assets

Supplementary material from the paper’s appendix.

Appendix

Parameter	Value
Temporal patch size ( $P$ )	8
Number of 3D Transformer blocks ( $L$ )	12
Number of heads	6
Embedding dimension ( $D$ )	192
Feed-forward dimension	768
Output dimension ( $K$ )	5000

Appendix

Table 6: Baguan-TS model architecture hyperparameters.

Panel of Figure 12 — Figure 12: Joint residual distributions for the energy task proenfo_gfc14 , the retail task rossmann_1W , and the aggregated results across all 30 tasks. Darker blue bins indicate higher data density. Points lying along the red dashed identity line ( $y=x$ ) correspond to instances where prediction errors are equal in both modes. Deviations from this diagonal, particularly in the second and fourth quadrants, reveal complementary error patterns between the two modes.

Figure 13: Calibration histograms of ground-truth quantile levels in predicted CDFs for different inference modes on epf_de (energy task).

Figure 14: Calibration histograms of ground-truth quantile levels in predicted CDFs for different inference modes on hermes (retail task).

Figure 15: Calibration histograms of ground-truth quantile levels in predicted CDFs for different inference modes on fev-bench-cov dataset (across all 30 tasks).

Figure 16: Toy periodic spike data generated using

f(t)=\exp(k\cdot(\sin(\frac{2\pi t}{50})-1))

. A larger

k

value results in a sharper periodic spike signal.

Panel of Figure 17 — Figure 17: Attention weight maps on the synthetic spike series for the baseline model (w/o overfitting) and the context-overfitting model (with overfitting). Each subplot overlays the ground-truth signal, model predictions, and the corresponding attention distribution within the context window at the query step (orange dash–dot line).

Panel of Figure 18 — Figure 18: Point forecasting evaluation on fev-bench-cov .

Figure 19: Probabilistic forecasting evaluation on fev-bench- cov using WQL.

Figure 20: Skill score comparison on fev-bench-cov , using Seasonal Naive as the baseline model.

Task	Domain	Frequency	# items	median length	# obs	# known dynamic cols	H	W	# seasonality	# targets
entsoe_15T	energy	15 Min	6	175,292	6,310,512	3	96	20	96	1
entsoe_1H	energy	1 H	6	43,822	1,577,592	3	96	20	48	1
entsoe_30T	energy	30 Min	6	87,645	3,155,220	3	168	20	24	1
epf_be	energy	1 H	1	52,416	157,248	2	24	20	24	1
epf_de	energy	1 H	1	52,416	157,248	2	24	20	24	1
epf_fr	energy	1 H	1	52,416	157,248	2	24	20	24	1

Appendix

Table 7: Detailed overview of the 30 covariate-aware tasks from the fev-bench benchmark, collectively referred to as fev-bench-cov .

	gfc12				gfc14				gfc17
Model	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL
AutoARIMA	1.1408	1.3848	0.1193	0.0987	0.9471	1.1681	0.0571	0.0464	1.1150	1.3821	0.0943	0.0762
AutoETS	2.4309	2.8114	0.2331	0.2073	1.1104	1.3186	0.0647	0.0545	2.1346	2.4128	0.1663	0.1466
AutoTheta	1.4149	1.5237	0.1360	0.1251	1.0555	1.1857	0.0580	0.0519	1.1470	1.3687	0.0931	0.0770
Chronos-Bolt	0.9172	1.0781	0.0910	0.0773	0.7674	0.9285	0.0455	0.0376	0.9004	1.0977	0.0745	0.0608
Moirai-2.0	0.7928	0.9538	0.0803	0.0668	0.6766	0.8458	0.0413	0.0330	0.7740	0.9628	0.0647	0.0519

Appendix

Table 8: Performance Comparison on proenfo_gfc12 , proenfo_gfc14 , and proenfo_gfc17 . The best results are highlighted in bold , and the second-best results are underlined .

	sales_1D				orders_1D				sales_1W				orders_1W
Model	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL
AutoARIMA	1.2758	1.5092	0.4095	0.3459	1.2662	1.5624	0.0741	0.0604	1.8025	2.0379	0.3070	0.2670	1.4147	1.7324	0.0584	0.0471
AutoETS	1.2662	1.4986	0.4185	0.3543	1.4470	1.4870	0.0657	0.0637	14.4532	1.8900	0.3003	4.0491	1.4190	1.7583	0.0582	0.0469
AutoTheta	1.2818	1.4939	0.4131	0.3563	1.3973	1.5185	0.0664	0.0607	1.6547	1.8364	0.2946	0.2656	1.3963	1.7122	0.0573	0.0465
Chronos-Bolt	1.1471	1.3871	0.3783	0.3140	1.0508	1.3016	0.0614	0.0495	1.5216	1.8467	0.2846	0.2337	1.4282	1.7219	0.0570	0.0471
Moirai-2.0	1.1696	1.4021	0.3821	0.3202	0.9700	1.1761	0.0552	0.0455	1.5157	1.8215	0.2871	0.2365	1.5315	1.8740	0.0612	0.0501

Appendix

Table 9: Performance Comparison on rohlik_sales_1D , rohlik_orders_1D , rohlik_sales_1W , and rohlik_orders_1W . The best results are highlighted in bold , and the second-best results are underlined .

	15T				30T				1H
Model	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL
AutoARIMA	—	—	—	—	0.9807	1.2299	0.0909	0.0732	0.8725	1.1176	0.0854	0.0667
AutoETS	3.0289	4.0070	0.4081	0.3140	2.4928	3.2738	0.2412	0.1816	1.9050	2.0475	0.1570	0.1447
AutoTheta	0.5794	0.7298	0.0540	0.0430	0.7997	1.0040	0.0721	0.0572	0.9723	1.1626	0.0836	0.0694
Chronos-Bolt	0.5062	0.6062	0.0428	0.0363	0.5294	0.6326	0.0378	0.0321	0.4574	0.5564	0.0341	0.0282
Moirai-2.0	0.4783	0.5933	0.0424	0.0343	0.4884	0.5974	0.0383	0.0318	0.4871	0.5924	0.0396	0.0333

Appendix

Table 10: Performance Comparison on entsoe_15T , entsoe_30T , and entsoe_1H . The best results are highlighted in bold , and the second-best results are underlined .

	be				de				fr				np				pjm
Model	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL
AutoARIMA	1.0561	1.0948	0.1986	0.1868	1.2777	1.6231	0.6819	0.5433	1.1581	0.9888	0.1532	0.1715	1.3932	1.7096	0.0786	0.0637	0.4819	0.5573	0.0985	0.0855
AutoETS	1.5343	1.3929	0.2488	0.2659	1.4013	1.7417	0.6107	0.5288	0.8989	0.9665	0.1493	0.1387	1.9332	2.3244	0.1041	0.0864	0.9139	0.9847	0.1717	0.1607
AutoTheta	1.4843	1.0194	0.1882	0.2582	1.4944	1.4072	0.6460	0.6490	1.5912	0.8447	0.1294	0.2296	1.2812	1.5140	0.0688	0.0579	0.6032	0.6832	0.1199	0.1068
Chronos-Bolt	0.5731	0.7273	0.1357	0.1069	1.0208	1.2655	0.5607	0.4644	0.4389	0.5638	0.0877	0.0685	0.9711	1.2409	0.0567	0.0445	0.4217	0.5357	0.0938	0.0739
Moirai-2.0	0.5281	0.6709	0.1228	0.0968	1.0164	1.2282	0.5365	0.4586	0.4092	0.5035	0.0791	0.0646	0.9253	1.1998	0.0543	0.0420	0.4405	0.5631	0.0976	0.0766

Appendix

Table 11: Performance Comparison on epf_be , epf_de , epf_fr , epf_np , and epf_pjm . The best results are highlighted in bold , and the second-best results are underlined .

	rossmann_1D				rossmann_1W				hermes				walmart
Model	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL
AutoARIMA	0.5619	0.6544	0.2224	0.1908	0.5212	0.6689	0.1836	0.1410	1.2129	1.5317	0.0064	0.0050	1.0205	1.2474	0.1596	0.1320
AutoETS	0.5937	0.6913	0.2361	0.2028	0.5175	0.6685	0.1836	0.1402	1.6730	1.9852	0.0088	0.0074	-	1.7227	0.2951	-
AutoTheta	0.8315	0.7448	0.2558	0.2910	0.5160	0.6644	0.1813	0.1385	1.5539	1.8478	0.0081	0.0068	1.4675	1.4179	0.1852	0.1997
Chronos-Bolt	0.5246	0.6371	0.2176	0.1788	0.4871	0.6452	0.1760	0.1317	0.6752	0.8579	0.0032	0.0025	0.7740	0.9671	0.1173	0.0950
Moirai-2.0	0.5274	0.6480	0.2215	0.1799	0.4969	0.6440	0.1759	0.1342	0.7038	0.8854	0.0034	0.0027	0.8447	1.0559	0.1315	0.1058

Appendix

Table 12: Performance Comparison on rossmann_1D , rossmann_1W , hermes , and walmart . The best results are highlighted in bold , and the second-best results are underlined .

	1D				1W				1M
Model	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL
AutoARIMA	0.8517	1.0631	0.7717	0.6115	0.9367	1.1568	0.4388	0.3580	1.0455	1.2131	0.4601	0.3801
AutoETS	0.8528	1.0633	0.7714	0.6156	0.9531	1.1672	0.4468	0.3728	1.1082	1.2139	0.4605	0.4321
AutoTheta	0.8721	1.0806	0.7779	0.6265	0.9634	1.1698	0.4475	0.3767	1.0987	1.2590	0.4910	0.4195
Chronos-Bolt	0.7293	0.8852	0.7110	0.5620	0.9165	1.1647	0.4334	0.3410	1.0001	1.1852	0.4455	0.3566
Moirai-2.0	0.7096	0.8691	0.6984	0.5508	0.9069	1.1501	0.4286	0.3361	0.9959	1.1773	0.4363	0.3457

Appendix

Table 13: Performance Comparison on m5_1D , m5_1W , and m5_1M . The best results are highlighted in bold , and the second-best results are underlined .

	stores_1D				stores_1W				stores_1M				transactions_1D
Model	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL
AutoARIMA	1.2216	1.4188	0.1934	0.1647	2.2969	2.5801	0.1501	0.1331	2.0382	2.2075	0.1385	0.1314	1.5622	1.7409	0.1205	0.1055
AutoETS	1.2379	1.3799	0.1872	0.1672	2.3568	2.5165	0.1484	0.1430	1.9424	2.1221	0.1568	0.1329	1.1813	1.2765	0.1010	0.0945
AutoTheta	1.2732	1.3759	0.1835	0.1779	2.3160	2.4768	0.1444	0.1408	1.9416	2.1335	0.1535	0.1245	1.2463	1.2511	0.0961	0.0991
Chronos-Bolt	1.0322	1.2689	0.1743	0.1419	2.1011	2.4749	0.1580	0.1268	2.0865	2.4178	0.2637	0.1852	0.9750	1.1515	0.0873	0.0736
Moirai-2.0	0.9798	1.2047	0.1568	0.1279	2.1965	2.5773	0.1555	0.1243	2.0913	2.3236	0.2355	0.1726	1.1211	1.3295	0.0837	0.0705

Appendix

Table 14: Performance Comparison on favorita_stores (1D/1W/1M) and favorita_transactions_1D . The best results are highlighted in bold , and the second-best results are underlined .

	15T				1H
Model	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL
AutoARIMA	—	—	—	—	1.1314	1.1133	1.2902	1.2703
AutoETS	2.5289	2.4162	1.4215	1.9572	2.1818	2.2682	1.1465	1.3928
AutoTheta	3.5851	1.2729	1.5023	3.2873	3.3576	1.5354	1.5474	2.6715
Chronos-Bolt	0.8094	0.9765	1.2911	1.1301	0.8157	1.0720	1.3260	1.0190
Moirai-2.0	0.8387	1.0764	1.3761	1.1205	0.9071	1.1358	1.4828	1.2285

Appendix

Table 15: Performance Comparison on solar_with_weather_15T and solar_with_weather_1H . The best results are highlighted in bold , and the second-best results are underlined .

	1H				1D
Model	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL
AutoARIMA	1.1924	1.3698	0.4518	0.3924	1.2403	1.5585	0.3229	0.2530
AutoETS	4.10 $\times 10^{5}$	10.6979	4.0642	2.05 $\times 10^{5}$	1.1813	1.3629	0.2791	0.2425
AutoTheta	1.9560	1.3458	0.4168	0.6724	1.2334	1.4428	0.2964	0.2579
Chronos-Bolt	0.8990	1.1162	0.3758	0.3020	1.0920	1.3887	0.2843	0.2229
Moirai-2.0	0.9454	1.1965	0.3904	0.3063	1.1380	1.4417	0.2916	0.2299

Appendix

Table 16: Performance Comparison on uci_air_quality_1H and uci_air_quality_1D . The best results are highlighted in bold , and the second-best results are underlined .

	Load datasets (18)				Photovoltaic datasets (9)				All real-world application datasets (27)
Model	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL
AutoARIMA	2.5730	0.8526	0.0395	0.1289	3.5350	0.7858	0.2366	1.0570	2.8936	0.8303	0.1052	0.4383
AutoETS	7.4514	6.4652	0.2931	0.3218	22.4679	5.7401	1.7096	6.7013	12.4569	6.2235	0.7653	2.4483
AutoTheta	0.8977	1.2644	0.0632	0.0385	38.8877	6.6861	1.9921	11.5991	13.5611	3.0717	0.7062	3.8920
Chronos-Bolt	0.4415	0.5491	0.0253	0.0203	0.6471	0.8066	0.2424	0.1945	0.5101	0.6350	0.0976	0.0783
Moirai-2.0	0.7621	0.9701	0.0460	0.0360	0.6175	0.7222	0.2175	0.1859	0.7139	0.8875	0.1031	0.0860

Appendix

Table 17: Average results on load, photovoltaic, and all real application datasets. The best results are highlighted in bold , and the second-best results are underlined .

Task	Domain	Frequency	# items	median length	# obs	# known dynamic cols	H	W	# seasonality	# targets
ETT_15T	energy	15 Min	2	69,680	975,520	0	96	20	96	7
ETT_1H	energy	1 H	2	17,420	243,880	0	168	20	24	7
bizitobs_l2c_5T	cloud	5 Min	1	31,968	223,776	0	288	20	288	7
boomlet_619	cloud	1 Min	1	16,384	851,968	0	60	20	1440	52
boomlet_1282	cloud	1 Min	1	16,384	573,440	0	60	20	1440	35
boomlet_1676	cloud	30 Min	1	10,463	1,046,300	0	96	20	48	100

Appendix

Table 18: Summary of the 10 representative univariate forecasting tasks selected from fev-bench-mini , collectively referred to as fev-bench-uni . Datasets with multiple targets (# targets

>1

) are decomposed into independent univariate series for evaluation.

Model	SQL	MASE	WAPE	WQL
Chronos-Bolt	0.6083	0.7369	0.3974	0.3438
Moirai-2.0	0.5405	0.6728	0.3254	0.2735
Sundial-Base	0.5814	0.6833	0.3338	0.2902
TabPFN-TS	0.5920	0.7364	0.3384	0.2685
TimesFM-2.5	0.5428	0.6831	0.3341	0.2726
TiRex	0.5684	0.7104	0.3858	0.3215

Appendix

Table 19: Average results on fev-bench-uni . The best results are highlighted in bold .

Figure 21: Probabilistic forecasting evaluation on fev-bench-uni using WAPE and WQL.

	15T				1H
Model	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL
AutoARIMA	—	—	—	—	1.0524	1.2616	0.2730	0.2275
AutoETS	1.2626	1.4293	0.2090	0.1890	1.7645	1.6021	0.3240	0.3554
AutoTheta	1.0985	0.8022	0.1328	0.1702	2.0613	1.2847	0.2708	0.3879
Chronos-Bolt	0.5737	0.7033	0.1146	0.0933	0.9436	1.1267	0.2465	0.2059
Moirai-2.0	0.5634	0.7119	0.1160	0.0915	0.8993	1.1240	0.2470	0.1952

Appendix

Table 20: Performance Comparison on ETT_15T and ETT_1H . The best results are highlighted in bold , and the second-best results are underlined .

	1D				1W
Model	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL
AutoARIMA	0.5556	0.7209	0.5348	0.4122	0.5793	0.7541	0.2123	0.1631
AutoETS	0.5558	0.7211	0.5350	0.4123	0.5783	0.7541	0.2123	0.1628
AutoTheta	0.5748	0.7429	0.5510	0.4264	0.5977	0.7779	0.2191	0.1683
Chronos-Bolt	0.5562	0.7195	0.5337	0.4125	0.5868	0.7623	0.2146	0.1653
Moirai-2.0	0.5556	0.7188	0.5332	0.4121	0.5862	0.7643	0.2153	0.1652

Appendix

Table 21: Performance Comparison on hospital_admissions_1D and hospital_admissions_1W . The best results are highlighted in bold , and the second-best results are underlined .

	619				1676				1282
Model	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL
AutoARIMA	0.5545	0.7170	0.5880	0.4527	—	—	—	—	0.5565	0.5925	0.4050	0.3750
AutoETS	0.8944	1.0938	0.9529	0.7636	0.7564	0.7610	0.3540	0.3561	0.9136	0.6890	0.4705	0.6261
AutoTheta	0.8352	1.0200	0.8821	0.6993	0.7835	0.7772	0.3606	0.3690	0.9717	0.6910	0.4718	0.6673
Chronos-Bolt	0.4709	0.5941	0.4683	0.3764	0.6077	0.7192	0.3289	0.2758	0.4618	0.5647	0.3918	0.3174
Moirai-2.0	0.3294	0.4306	0.3062	0.2356	0.5727	0.7128	0.3274	0.2580	0.4269	0.5230	0.3639	0.2944

Appendix

Table 22: Performance Comparison on boomlet_619 , boomlet_1676 , and boomlet_1282 . The best results are highlighted in bold , and the second-best results are underlined .

	bizitobs_l2c_5T				jena_weather_1H				M_DENSE_1D
Model	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL	SQL	MASE	WAPE	WQL
AutoARIMA	0.8247	0.9163	1.5980	1.8772	0.4370	0.5092	0.9375	0.8257	0.9702	1.1690	0.1261	0.1051
AutoETS	0.7311	0.8137	1.3367	1.6114	0.5529	0.5678	0.3522	1.4085	1.0735	1.0869	0.1301	0.1324
AutoTheta	0.7496	0.8740	1.6561	1.6069	0.5933	0.4846	0.2955	1.6859	1.1435	1.0772	0.1322	0.1459
Chronos-Bolt	0.7570	0.8002	1.3254	1.2750	0.3668	0.4543	0.2519	0.2341	0.7590	0.9249	0.0985	0.0817
Moirai-2.0	0.3675	0.4035	0.7997	0.7682	0.3652	0.4505	0.2487	0.2342	0.7390	0.8884	0.0962	0.0807

Appendix

Table 23: Performance Comparison on bizitobs_l2c_5T , jena_weather_1H , and M_DENSE_1D . The best results are highlighted in bold , and the second-best results are underlined .

Time Series Forecasting

Time series forecasting predicts future values from ordered observations using statistical, neural, and probabilistic models to support decisions under uncertainty.

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TS-ICL: A Flexible Time-Indexed Foundation Model for Time Series via In-Context Learning

Etienne Le Naour, Tahar Nabil, Adrien Petralia

1EDF R&D, Palaiseau, France

Irregular Time-Series Modeling Time Series Imputation Time Series Forecasting In-Context Learning Time-Series Foundation Models Probabilistic Time Series Forecasting

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Foundation models mark a profound paradigm shift in time series modeling, with task-specific models being superseded by general-purpose zero-shot models. Yet, current approaches primarily focus on forecasting, while real-world time series are often irregularly and partially observed, requiring models that can jointly forecast, impute missing values, and handle degraded sampling conditions. To address these challenges, we introduce TS-ICL, a novel probabilistic In-Context Learning encoder--regressor Transformer that unifies forecasting and imputation. TS-ICL formulates time series tasks as timestamp-aligned regression and naturally incorporates covariates by training on synthetic dependency structures generated from a novel causal data prior. Empirically, TS-ICL achieves a new state-of-the-art in imputation, while remaining competitive with leading forecasting foundation models across both univariate and covariate-aware benchmarks. It shows particularly strong performance in forecasting with partially observed look-back windows.

Abstract

Time Series Forecasting

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