SGA: Uncertainty Quantification for Multi-Step Forecasting in Time Series Foundation Models

Xin-Yu Hu; Shuang Liang; Cheng Feng; Shao-Qun Zhang

cs.LGSep 23, 2026

SGA: Uncertainty Quantification for Multi-Step Forecasting in Time Series Foundation Models

Authors: Xin-Yu Hu, Shuang Liang, Cheng Feng, Shao-Qun Zhang

Organizations: National Key Laboratory for Novel Software Technology, Nanjing University, China. · School of Intelligent Science and Technology, Nanjing University, China. · Siemens Data and AI Research, Beijing, China. · Nanjing University – Siemens Joint Research Center on Industrial AI, Suzhou, China.

Abstract

The recent emergence of Time Series Foundation Models (TSFMs) has significantly advanced multi-step forecasting performance, enabling accurate predictions over extended future horizons. However, existing TSFMs often suffer from significantly inherent uncertainty, which typically manifests as derived forecast branches emerging at each time step and spreading to subsequent steps; different forecast branches often exhibit varying forecasting performance, thereby undermining the credibility of TSFM forecasts. In this paper, we propose the Slicing-Graphing-Alignment (SGA) method to quantify the uncertainty of multi-step TSFM forecasts. The proposed SGA first characterizes the topology of all potential forecast branches using a directed acyclic graph, such that the graph complexity bounds the uncertainty of multi-step forecasts, and then precisely measures the graph complexity by integrating both topological information and TSFM-inherent stochasticity. Experimental results conducted on 11 TSFMs and 27 datasets demonstrate that (i) SGA achieves the best performance when ranking predictive errors with uncertainty estimates; (ii) SGA works with a more extensive and more precise sampling coverage than those of existing UQ methods, deriving a quantification mechanism fundamentally different from those of established ones; and (iii) larger model scales of TSFMs correlate with lower uncertainty estimates of multi-step forecasts, suggesting another empirical scaling law for uncertainty quantification of multi-step TSFM forecasts.

Figures & tables

Figure 1 : Workflow of time series multi-step forecasting and horizon uncertainty quantification.

UQ	Vocabulary-based					Quantile-based				Trajectory-based
UQ	C-T5-Tiny	C-T5-Mini	C-T5-Small	C-T5-Base	C-T5-Large	C-2-Small	C-2	TimesFM-2.5	Timer-S1	Sundial	Aurora
Rnd	100.00 0.00 0	100.00 0.00 0	100.00 0.00 0	100.00 0.00 0	100.00 0.00 0	100.00 0.00 0	100.00 0.00 0	100.00 0.00 0	100.00 0.00 0	100.00 0.00 0	100.00 0.00 0
NC	93.72 11.01	100.31 9.74 0	94.93 10.75	95.22 11.09	97.99 11.81	88.23 10.79	89.81 11.59	93.94 12.00	96.99 10.70	93.93 11.37	100.31 10.35
Ppl	89.33 11.52	87.81 10.24	92.21 12.82	88.88 12.16	93.43 11.42	86.91 10.55	84.74 10.41	87.03 11.81	93.11 9.96 0	93.46 11.14	100.14 10.89
PE	84.20 11.62	84.61 9.14 0	90.89 12.66	89.47 10.44	91.77 11.86	91.21 10.53	88.80 11.21	88.10 11.64	93.91 10.14	96.07 11.91	101.83 10.77
Eig	96.73 11.65	99.70 10.54	95.01 10.73	94.55 10.76	97.62 11.35	90.93 10.77	91.37 11.27	99.21 11.88	96.23 10.33	98.10 11.94	102.20 11.10

Table 1 : Comparisons of the overall NEAURC of SGA and its contenders, averaged across 27 datasets and 11 TSFMs of 3 types, where bold and underlined values denote the best and second-best results, respectively.

Figure 2 : Visualized comparisons of the sampling coverage between SGA and NC across 11 TSFMs of 3 types.

Type	TSFM	$\tfrac{A_{\text{SGA}}\cap A_{\text{NC}}}{A_{\text{NC}}}$	$\tfrac{A_{\text{SGA}}\cap A_{\text{NC}}}{A_{\text{SGA}}}$
Vocabulary-based	C-T5-Tiny	100.00	50.24
	C-T5-Mini	100.00	49.47
	C-T5-Small	100.00	48.68
	C-T5-Base	100.00	48.75
	C-T5-Large	100.00	48.77
Quantile-based	C-2-Small	91.40	93.51

Table 2 : Comparisons of the overall overlap area ratios for 11 TSFMs of 3 types, averaged across 27 datasets.

Figure 3 : Plots of averaged uncertainty versus ARMASE of TSFMs over diverse scales, averaged across 27 datasets.

Figure 4 : Ablation comparison of the overall performance of SGA on 11 TSFMs of 3 types, averaged across 27 datasets.

Figure 5 : Impact of the number of samples $K$ (left), the slicing length $l_{s}$ (middle), and the threshold coefficient $\lambda$ (right) on the overall performance of SGA for 11 TSFMs of 3 types, averaged across 27 datasets.

Appendix figures & tables21 assets

Supplementary material from the paper’s appendix.

Appendix

Category	Abbr.	Full Name	Multiple	Exploiting Inherent	Literature
Category	Abbr.	Full Name	Sampling?	Stochasticity?	Literature
Information-based	Ppl	Perplexity	$\times$	$\checkmark$	Fomicheva et al. (2020)
Information-based	PE	Predictive Entropy	$\checkmark$	$\checkmark$	Malinin and Gales (2021)
Diversity-based	SE	Semantic Entropy	$\checkmark$	$\checkmark$	Farquhar et al. (2024)
	SAR	Shifting Attention to Relevance	$\checkmark$	$\checkmark$	Duan et al. (2024)
	SD	Semantic Density	$\checkmark$	$\checkmark$	Qiu and Miikkulainen (2024)

Appendix

Table 3 : Overview of the UQ contenders for LLMs.

UQ for LLMs	HUQ for TSFMs
Token sequence	Forecast trajectory
Token	Forecast value
Token-level distribution	Time-step-level distribution
Semantic equivalence	DTW-based equivalence
Semantic similarity	DTW-based similarity

Appendix

Table 4 : Correspondence between the key elements used in UQ for LLMs and HUQ for TSFMs.

Figure 6 : Overall evaluation ranking of 10 UQ methods across 27 datasets and 11 TSFMs.

Dataset	NC	Ppl	PE	Eig	Ecc	Deg	SD	SAR	SE	SGA
Australian Electricity	0 88.70 52.20	0 91.40 62.00	0 77.40 51.60	121.70 51.00	107.00 41.90	121.70 50.50	0 91.40 61.50	105.10 52.50	0 77.40 49.90	0 26.80 43.30
CIF 2016	138.30 21.80	176.40 38.10	136.50 30.10	132.40 17.50	126.70 20.70	132.50 17.80	169.80 37.10	128.90 19.20	135.30 30.20	0 50.10 11.40
Car Parts	118.00 4.40 0	101.80 3.70 0	121.20 4.60 0	137.60 6.00 0	142.20 6.30 0	137.70 5.70 0	129.50 5.80 0	123.70 4.50 0	121.20 4.20 0	0 57.10 1.70 0
Covid Deaths	0 76.20 13.30	0 59.10 10.70	0 79.80 17.90	0 89.70 15.70	0 95.60 15.60	0 87.60 16.30	0 72.20 8.00 0	0 93.00 17.00	0 83.70 17.00	0 56.70 12.70
Dominick	0 32.90 0.90 0	0 65.20 0.90 0	0 33.90 0.80 0	0 35.90 1.00 0	0 35.90 1.00 0	0 34.50 0.90 0	0 35.40 1.00 0	0 32.70 0.80 0	0 33.80 0.80 0	0 29.80 0.90 0
ERCOT Load	128.40 32.30	117.50 32.50	0 74.10 30.50	0 91.80 46.90	0 46.90 34.30	0 91.80 47.60	117.50 34.10	0 73.10 41.00	0 74.10 30.70	0 75.60 28.90

Appendix

Table 5 : Comparisons of NEAURC of SGA and its contenders across 27 datasets for Chronos-T5-Tiny, where bold and underlined values denote the best and second-best results, respectively.

Dataset	NC	Ppl	PE	Eig	Ecc	Deg	SD	SAR	SE	SGA
Australian Electricity	182.70 38.60	106.50 49.40	0 9.10 11.70	187.40 27.30	0 76.70 43.90	187.40 20.80	106.50 69.00	187.40 25.30	0 9.10 11.00	118.00 59.10
CIF 2016	131.80 16.30	111.40 15.00	128.20 26.50	119.60 15.40	100.80 10.20	119.70 16.00	111.20 13.90	121.40 16.40	129.90 27.80	0 37.70 6.60 0
Car Parts	120.10 4.30 0	114.40 3.90 0	130.20 5.00 0	146.70 6.30 0	139.40 6.50 0	146.40 6.30 0	137.40 6.00 0	131.90 5.20 0	127.40 4.20 0	0 57.30 1.40 0
Covid Deaths	0 87.30 12.90	0 59.70 11.50	0 69.30 13.70	0 81.70 12.80	0 81.60 12.80	0 81.00 12.90	0 60.20 36.80	0 77.60 13.20	0 75.60 14.30	0 49.70 8.40 0
Dominick	0 32.70 0.90 0	0 63.50 1.00 0	0 37.70 1.20 0	0 38.20 1.00 0	0 37.80 1.00 0	0 37.40 1.00 0	0 34.70 1.00 0	0 37.00 1.20 0	0 37.90 1.20 0	0 31.00 1.00 0
ERCOT Load	100.00 38.50	0 87.10 38.70	0 91.80 42.00	117.90 40.50	0 58.10 33.30	117.90 38.80	0 74.70 35.10	0 93.60 43.60	0 91.80 42.50	0 25.20 11.80

Appendix

Table 6 : Comparisons of NEAURC of SGA and its contenders across 27 datasets for Chronos-T5-Mini, where bold and underlined values denote the best and second-best results, respectively.

Dataset	NC	Ppl	PE	Eig	Ecc	Deg	SD	SAR	SE	SGA
Australian Electricity	0 69.00 41.20	0 71.70 48.60	0 85.40 43.40	0 52.30 35.90	0 95.60 46.60	0 52.30 36.60	0 71.70 47.20	0 52.30 36.70	0 85.40 42.30	0 12.40 18.80
CIF 2016	114.50 16.40	156.90 35.10	118.70 28.70	121.00 15.90	108.90 14.50	121.00 16.40	159.20 36.90	115.30 16.20	117.80 29.10	0 26.80 5.30 0
Car Parts	125.20 5.60 0	118.00 3.90 0	128.50 5.40 0	139.70 6.30 0	132.50 6.20 0	139.50 6.30 0	134.80 6.30 0	130.30 5.60 0	126.30 4.60 0	0 60.20 1.60 0
Covid Deaths	0 83.20 12.70	0 73.30 16.30	0 65.70 11.60	0 82.10 8.90 0	0 80.80 8.90 0	0 81.90 9.30 0	0 76.20 9.30 0	0 82.50 10.80	0 73.30 11.30	0 58.30 15.50
Dominick	0 33.60 0.90 0	0 62.70 1.00 0	0 37.90 1.10 0	0 39.10 1.00 0	0 36.90 1.00 0	0 36.70 1.00 0	0 35.30 1.00 0	0 37.40 1.20 0	0 38.30 1.10 0	0 31.20 1.10 0
ERCOT Load	119.60 39.60	0 90.80 39.00	101.60 36.10	132.80 40.40	121.60 30.20	132.80 39.40	0 96.30 43.10	124.20 39.10	101.60 36.00	0 21.30 15.80

Appendix

Table 7 : Comparisons of NEAURC of SGA and its contenders across 27 datasets for Chronos-T5-Small, where bold and underlined values denote the best and second-best results, respectively.

Dataset	NC	Ppl	PE	Eig	Ecc	Deg	SD	SAR	SE	SGA
Australian Electricity	0 89.60 54.50	118.40 54.30	119.70 42.10	0 68.10 46.70	148.50 46.00	0 68.10 46.30	118.40 54.20	0 83.20 53.70	119.70 42.40	111.90 44.10
CIF 2016	117.70 16.30	109.80 26.20	101.00 21.20	109.00 15.60	0 93.00 13.50	109.10 16.00	111.10 27.30	103.80 16.90	101.50 21.60	0 33.70 6.30 0
Car Parts	132.80 5.10 0	119.30 3.70 0	130.20 5.00 0	141.30 6.70 0	133.30 6.80 0	141.70 6.70 0	140.90 6.40 0	132.80 5.50 0	132.90 5.10 0	0 67.30 1.90 0
Covid Deaths	0 91.90 10.00	0 64.00 10.60	0 75.10 10.50	0 97.70 11.00	0 96.40 12.20	0 95.10 10.80	0 69.30 25.00	0 86.40 11.20	0 79.70 10.10	0 53.20 8.50 0
Dominick	0 33.20 0.90 0	0 59.30 1.00 0	0 41.00 1.30 0	0 40.00 1.10 0	0 37.80 1.00 0	0 38.10 1.00 0	0 35.40 1.00 0	0 39.90 1.30 0	0 41.40 1.30 0	0 31.60 1.00 0
ERCOT Load	110.50 40.40	0 98.70 41.80	0 64.20 22.70	109.50 39.30	0 64.40 31.20	109.50 38.20	0 98.70 42.70	100.30 40.90	0 64.20 22.90	0 26.80 13.50

Appendix

Table 8 : Comparisons of NEAURC of SGA and its contenders across 27 datasets for Chronos-T5-Base, where bold and underlined values denote the best and second-best results, respectively.

Dataset	NC	Ppl	PE	Eig	Ecc	Deg	SD	SAR	SE	SGA
Australian Electricity	100.50 45.70	142.80 44.10	116.90 56.10	0 85.10 47.20	0 89.60 48.50	0 85.10 47.20	142.80 42.70	0 85.10 46.00	116.90 55.90	0 44.90 51.60
CIF 2016	121.30 17.10	176.10 36.40	115.30 24.70	107.60 15.00	136.30 21.10	107.60 15.40	176.40 37.90	103.90 15.90	114.90 26.20	0 36.90 6.60 0
Car Parts	126.00 5.30 0	113.50 3.60 0	130.40 4.70 0	142.40 6.40 0	140.10 7.00 0	142.60 6.50 0	136.50 5.90 0	132.00 4.70 0	126.90 4.10 0	0 60.90 1.50 0
Covid Deaths	102.80 12.70	0 81.10 16.60	0 93.50 17.40	102.30 14.30	100.60 13.20	102.90 14.90	0 81.40 19.50	0 99.30 15.30	0 87.10 13.70	0 68.20 10.70
Dominick	0 32.20 0.90 0	0 59.90 1.00 0	0 39.00 1.30 0	0 37.90 1.00 0	0 36.60 1.00 0	0 36.30 1.00 0	0 33.90 1.00 0	0 37.90 1.30 0	0 39.50 1.40 0	0 29.90 1.00 0
ERCOT Load	143.50 51.30	0 41.80 22.70	100.50 30.00	101.10 44.10	125.30 33.00	101.10 44.20	0 53.00 27.50	101.10 44.80	100.50 31.40	120.20 44.90

Appendix

Table 9 : Comparisons of NEAURC of SGA and its contenders across 27 datasets for Chronos-T5-Large, where bold and underlined values denote the best and second-best results, respectively.

Dataset	NC	Ppl	PE	Eig	Ecc	Deg	SD	SAR	SE	SGA
Australian Electricity	0 63.40 42.30	0 63.40 44.60	120.40 43.20	120.40 42.40	129.80 43.60	120.40 41.30	0 52.00 38.30	120.40 42.80	120.40 43.50	0 21.20 36.90
CIF 2016	118.40 16.50	112.60 15.50	118.40 16.50	112.60 15.20	122.50 18.30	114.70 15.80	108.60 14.60	113.70 15.60	116.80 15.90	0 27.90 7.40 0
Car Parts	129.90 6.90 0	127.20 5.60 0	136.10 5.40 0	131.20 6.20 0	121.80 5.40 0	131.80 6.40 0	136.50 6.40 0	123.80 4.60 0	122.40 4.40 0	0 54.50 1.70 0
Covid Deaths	0 69.30 9.10 0	0 56.00 7.30 0	0 71.60 9.90 0	0 63.70 7.50 0	0 63.70 7.30 0	0 63.90 7.30 0	0 62.70 7.20 0	0 67.90 9.30 0	0 70.30 9.90 0	0 19.40 3.00 0
Dominick	0 48.50 2.50 0	0 36.10 0.70 0	0 50.80 1.30 0	0 48.10 2.40 0	0 46.40 2.40 0	0 47.30 2.40 0	0 39.40 1.20 0	0 51.60 0.70 0	0 46.40 0.80 0	0 29.80 1.00 0
ERCOT Load	140.70 40.50	142.00 41.90	144.60 42.20	118.20 40.70	0 9.60 40.00	118.20 38.90	126.10 29.50	144.60 41.40	144.60 42.80	0 66.70 40.30

Appendix

Table 10 : Comparisons of NEAURC of SGA and its contenders across 27 datasets for Chronos-2-Small, where bold and underlined values denote the best and second-best results, respectively.

Dataset	NC	Ppl	PE	Eig	Ecc	Deg	SD	SAR	SE	SGA
Australian Electricity	0 66.00 54.90	0 43.40 36.10	0 65.50 52.30	0 89.30 58.10	138.90 47.80	0 89.30 57.80	0 43.40 34.40	0 89.30 58.40	0 65.50 51.70	0 12.20 28.80
CIF 2016	111.50 15.70	100.60 15.90	105.40 14.50	106.60 14.80	113.40 16.00	106.70 15.00	0 94.20 13.80	106.60 15.20	105.20 14.70	0 24.90 5.40 0
Car Parts	117.90 5.60 0	109.90 4.00 0	130.90 5.30 0	123.20 5.50 0	114.20 4.60 0	123.70 5.60 0	124.50 4.30 0	116.50 4.40 0	120.70 4.20 0	0 54.60 1.70 0
Covid Deaths	0 70.00 8.50 0	0 54.20 9.40 0	0 55.90 8.60 0	0 63.70 7.00 0	0 62.80 7.00 0	0 63.80 6.80 0	0 63.60 8.00 0	0 54.50 6.80 0	0 51.50 6.00 0	0 21.70 3.40 0
Dominick	0 47.30 2.50 0	0 33.00 0.90 0	0 38.40 1.00 0	0 47.20 2.40 0	0 45.60 2.50 0	0 46.60 2.40 0	0 39.30 1.20 0	0 42.10 0.90 0	0 37.50 0.80 0	0 26.50 1.00 0
ERCOT Load	125.10 50.40	119.30 50.10	119.30 49.70	108.00 44.10	105.60 29.10	108.00 43.90	124.10 48.50	128.60 49.60	119.30 49.80	0 6.60 4.40 0

Appendix

Table 11 : Comparisons of NEAURC of SGA and its contenders across 27 datasets for Chronos-2, where bold and underlined values denote the best and second-best results, respectively.

Dataset	NC	Ppl	PE	Eig	Ecc	Deg	SD	SAR	SE	SGA
Australian Electricity	115.50 52.80	0 67.50 63.10	0 91.20 55.70	169.20 39.90	0 84.60 55.60	169.20 39.00	0 87.00 57.00	115.50 53.70	0 91.20 55.30	0 18.30 22.30
CIF 2016	122.90 18.80	101.00 15.70	0 99.50 16.20	123.10 17.50	143.30 23.50	125.40 19.20	101.60 16.80	108.60 18.80	105.80 20.10	0 29.40 5.10 0
Car Parts	142.50 7.50 0	0 97.90 3.10 0	0 98.10 3.90 0	136.70 6.20 0	133.10 6.60 0	136.70 6.40 0	111.40 4.20 0	0 87.90 2.90 0	0 86.80 2.80 0	0 54.80 1.60 0
Covid Deaths	0 71.70 8.10 0	0 37.80 4.70 0	0 53.70 7.00 0	0 77.00 9.10 0	0 81.70 9.70 0	0 77.80 9.20 0	0 59.70 5.80 0	0 49.80 5.00 0	0 59.40 7.90 0	0 16.20 2.40 0
Dominick	0 44.70 2.00 0	0 31.10 0.70 0	0 36.00 1.00 0	0 42.40 1.80 0	0 42.60 1.70 0	0 41.90 1.70 0	0 33.00 0.80 0	0 37.30 1.10 0	0 35.20 1.10 0	0 24.00 0.80 0
ERCOT Load	0 81.30 51.50	0 98.20 58.10	0 98.20 56.20	0 98.20 57.10	0 89.40 30.10	0 98.20 57.90	0 87.90 51.70	0 98.20 57.60	0 98.20 57.20	0 64.80 43.40

Appendix

Table 12 : Comparisons of NEAURC of SGA and its contenders across 27 datasets for TimesFM-2.5, where bold and underlined values denote the best and second-best results, respectively.

Dataset	NC	Ppl	PE	Eig	Ecc	Deg	SD	SAR	SE	SGA
Australian Electricity	0 90.00 57.40	0 81.00 53.90	0 92.40 57.60	0 92.40 58.20	133.80 57.30	0 92.40 58.00	107.60 46.30	0 92.40 58.80	0 92.40 57.70	0 8.90 14.50
CIF 2016	114.60 18.70	0 99.70 16.60	102.40 14.10	105.10 15.10	111.80 16.30	105.60 15.10	111.40 15.90	104.30 14.90	102.00 14.00	0 32.90 6.00 0
Car Parts	158.40 7.20 0	112.70 3.80 0	127.50 5.50 0	160.20 7.00 0	154.30 7.10 0	160.30 7.10 0	123.90 3.70 0	106.70 3.40 0	115.50 4.40 0	0 59.30 1.50 0
Covid Deaths	0 67.00 7.10 0	0 25.20 3.40 0	0 25.20 3.70 0	0 68.80 7.10 0	0 68.00 7.10 0	0 68.20 6.80 0	0 59.20 5.60 0	0 34.70 4.40 0	0 31.90 3.80 0	0 12.80 2.70 0
Dominick	0 47.10 2.40 0	0 32.20 1.00 0	0 35.20 1.00 0	0 48.10 2.40 0	0 45.70 2.50 0	0 47.30 2.30 0	0 37.80 1.30 0	0 37.40 1.00 0	0 36.50 1.20 0	0 27.00 1.10 0
ERCOT Load	0 90.80 39.30	125.60 37.20	0 82.20 40.30	0 66.90 34.30	0 74.00 34.60	0 66.90 34.80	117.40 48.30	0 85.60 41.70	0 82.20 39.00	0 44.00 26.10

Appendix

Table 13 : Comparisons of NEAURC of SGA and its contenders across 27 datasets for Timer-S1, where bold and underlined values denote the best and second-best results, respectively.

Dataset	NC	Ppl	PE	Eig	Ecc	Deg	SD	SAR	SE	SGA
Australian Electricity	122.00 53.60	125.00 51.60	125.00 53.00	111.50 52.30	132.90 70.40	111.50 53.00	149.40 47.10	125.00 53.10	125.00 51.80	0 72.40 43.30
CIF 2016	111.10 16.00	111.50 14.60	110.70 14.10	105.70 14.40	0 85.50 11.10	104.30 14.00	0 99.60 12.60	107.50 14.10	108.40 13.70	0 22.90 4.80 0
Car Parts	145.50 6.40 0	146.20 6.00 0	150.60 5.90 0	140.60 5.40 0	127.20 5.60 0	140.70 5.50 0	143.60 5.50 0	144.20 5.80 0	151.00 5.70 0	0 55.90 1.60 0
Covid Deaths	0 69.90 7.00 0	0 69.00 7.40 0	0 71.60 8.20 0	0 77.50 8.70 0	0 78.30 10.90	0 76.00 8.40 0	0 69.60 7.30 0	0 71.60 8.00 0	0 71.40 8.80 0	0 12.10 1.80 0
Dominick	0 51.90 2.40 0	0 51.50 2.60 0	0 52.60 2.40 0	0 56.00 2.40 0	0 52.60 2.20 0	0 53.90 2.30 0	0 52.60 2.50 0	0 54.70 2.50 0	0 53.00 2.50 0	0 25.10 0.90 0
ERCOT Load	126.30 43.50	153.30 48.30	0 93.30 40.10	119.00 46.20	109.00 35.20	119.00 46.30	114.50 45.30	121.10 45.50	0 93.30 40.40	0 98.90 32.40

Appendix

Table 14 : Comparisons of NEAURC of SGA and its contenders across 27 datasets for Sundial, where bold and underlined values denote the best and second-best results, respectively.

Dataset	NC	Ppl	PE	Eig	Ecc	Deg	SD	SAR	SE	SGA
Australian Electricity	173.40 26.00	152.40 43.60	154.60 40.40	152.40 43.10	152.40 43.00	152.40 42.60	152.40 42.30	152.40 47.70	154.60 41.50	0 26.60 25.30
CIF 2016	130.70 16.50	124.90 12.50	129.80 13.90	119.60 16.60	103.90 18.80	119.70 17.30	113.50 17.60	122.20 15.90	131.70 15.90	0 69.10 9.80 0
Car Parts	185.30 9.40 0	178.90 8.00 0	174.40 7.70 0	165.60 7.40 0	143.50 7.20 0	165.80 7.60 0	170.30 6.90 0	168.10 8.10 0	175.10 7.80 0	0 61.00 2.10 0
Covid Deaths	106.00 15.30	106.80 15.00	117.80 15.60	120.80 16.70	119.00 15.50	120.90 16.70	117.20 16.40	121.60 17.00	119.00 16.80	0 80.60 9.80 0
Dominick	0 76.00 1.70 0	0 76.50 1.60 0	0 77.10 1.60 0	0 76.70 1.40 0	0 76.10 1.40 0	0 75.50 1.40 0	0 73.00 1.50 0	0 76.10 1.60 0	0 76.90 1.60 0	0 42.90 0.30 0
ERCOT Load	0 86.80 43.10	0 91.40 44.60	0 91.40 44.40	0 95.80 46.90	0 59.60 36.40	0 95.80 46.70	0 84.70 32.40	0 95.80 46.40	0 91.40 42.90	0 53.70 23.40

Appendix

Table 15 : Comparisons of NEAURC of SGA and its contenders across 27 datasets for Aurora, where bold and underlined values denote the best and second-best results, respectively.

Figure 7 : Plots of averaged uncertainty versus MASE of TSFMs over diverse scales across 27 datasets.

Figure 8 : Ablation comparison of UQ performance of SGA on 11 TSFMs of 3 types over the first 9 datasets.

Figure 9 : Ablation comparison of UQ performance of SGA on 11 TSFMs of 3 types over the middle 9 datasets.

Figure 10 : Ablation comparison of UQ performance of SGA on 11 TSFMs of 3 types over the last 9 datasets.

Figure 11 : Impact of the number of samples $K$ on the performance of SGA across 27 datasets and 11 TSFMs of 3 types.

Figure 12 : Impact of the slicing length $l_{s}$ on the performance of SGA across 27 datasets and 11 TSFMs of 3 types.

Figure 13 : Impact of the threshold coefficient $\lambda$ on the performance of SGA across 27 datasets and 11 TSFMs of 3 types.

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Despite the success of Time Series Foundation Models (TSFMs) on broad benchmarks, their ability to internalize basic temporal logic, especially in settings supported by exogenous covariates, remains under-examined. We introduce SimpleTimeBench, a diagnostic univariate and multivariate "unit test" suite for primitives such as monotonic trends, periodic signals and leading indicator covariates, scenarios where near-perfect forecasts should be trivial. Surprisingly, prominent multivariate TSFMs (Chronos-2, Moirai and Toto) frequently produce suboptimal zero-shot forecasts for these inputs. While fine-tuning Chronos-2 improves its behaviour on specific tasks, we show that this adaptation degrades performance on other fundamental patterns rather than enhancing its generalizable foundational capabilities. This reveals a gap between pre-training scale and basic temporal reasoning, suggesting that current TSFMs could potentially lack the inductive biases needed to capture simple predictable functions. We further demonstrate that these failures are not merely synthetic curiosities: they persist in real-world sensor forecasting, where TSFMs consistently underutilize leading indicators available in observed covariates. This inability to capture simple relationships limits the practical utility and reliability of current multivariate models.

Abstract

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