Regression Models Meet Foundation Models: A Hybrid-AI Approach to Practical Electricity Price Forecasting

Yunzhong Qiu; Binzhu Li; Hao Wei; Shenglin Weng; Chen Wang; Zhongyi Pei; Mingsheng Long; Jianmin Wang

cs.LGMar 6, 2026

Regression Models Meet Foundation Models: A Hybrid-AI Approach to Practical Electricity Price Forecasting

Authors: Yunzhong Qiu, Binzhu Li, Hao Wei, Shenglin Weng, Chen Wang, Zhongyi Pei, Mingsheng Long, Jianmin Wang

Organizations: School of Software, BNRist, Tsinghua University, Beijing, China · Suzhou Industrial Park Xingzhixun CS Co., Ltd., Jiangsu, China

Abstract

Electricity market prices exhibit extreme volatility, nonlinearity, and non-stationarity, making accurate forecasting a significant challenge. While cutting-edge time series foundation models (TSFMs) effectively capture temporal dependencies, they typically underutilize cross-variate correlations and non-periodic patterns that are essential for price forecasting. Conversely, regression models excel at capturing feature interactions but are limited to future-available inputs, ignoring crucial historical drivers that are unavailable at forecast time. To bridge this gap, we propose FutureBoosting, a novel paradigm that enhances regression-based forecasts by integrating forecasted features generated from a frozen TSFM. This approach leverages the TSFM's ability to model historical patterns and injects these insights as enriched inputs into a downstream regression model. We instantiate this paradigm into a lightweight, plug-and-play framework for electricity price forecasting. Extensive evaluations on real-world electricity market data demonstrate that our framework consistently outperforms state-of-the-art TSFMs and regression baselines, achieving reductions in Mean Absolute Error (MAE) of more than 30% at most. Through ablation studies and explainable AI (XAI) techniques, we validate the contribution of forecasted features and elucidate the model's decision-making process. FutureBoosting establishes a robust, interpretable, and effective solution for practical market participation, offering a general framework for enhancing regression models with temporal context.

Figures & tables

Panel of Figure 1 — Figure 1. Electricity price characteristics in the Shanxi spot market (15-min). (a) Day-ahead vs real-time forecasts in a representative October 2025 window. (b) Price distribution over the full year 2025, showing heavy tails and extremes.

Indicator	Day-ahead	Real-time	Gaussian
Tail ratio $p99/p50$	4.86	5.33	$\approx$ 2 (1.5–2.5)
Extreme freq. $\mathbb{P}(p>1000)$	5.45%	5.88%	$\approx$ 0% ( $<$ 0.1%)
Excess kurtosis	5.05	5.39	0
Jump size $p99(\|\Delta p\|)$	399.8	439.9	$\approx 200(2.576\times\sigma_{\Delta p})$
Jump freq. $\mathbb{P}(\|\Delta p\|>200)$	2.92%	3.33%	$\approx$ 1% (0.5–1.5%)

Table 1. Key difficulty indicators of Shanxi electricity prices in 2025. Higher values indicate more challenging dynamics.

Figure 2. Illustration of electricity market trading background. Suppliers and consumers must provide day-ahead plans for day $D+1$ on day $D$ . More accurate forecasts from the AI model improve the trading plan’s foresight, yielding greater benefits.

Figure 3. Comparison of forecasting paradigms. Our FutureBoosting paradigm first forecasts future-unavailable exogenous variables using TSFM, then uses these augmented features, along with future-available exogenous variables, for regression-based target forecasting.

Figure 4. The pipeline of our FutureBoosting framework for electricity price forecasting. TSFM-augmented features, future available exogenous variables, and the grid production plan form an enriched feature set for downstream regression models.

Method

Day-ahead

Real-time

MSE

MAE

MSE

MAE

Val

\Delta

LGBM

\Delta

Val

\Delta

LGBM

\Delta

Val

\Delta

LGBM

\Delta

Val

\Delta

LGBM

\Delta

LGBM (ic27)

35658.52

0.00%

–

100.53

0.00%

–

49182.67

0.00%

–

121.63

0.00%

–

TimerXL

76278.90

-113.91%

–

162.69

-61.83%

–

86353.72

-75.58%

–

171.63

-41.11%

–

+ FutureBoosting

33978.45

+4.71%

+55.45%

94.78

+5.72%

+41.74%

44522.21

+9.48%

+48.44%

117.10

+3.72%

+31.77%

Sundial

62979.60

-76.62%

–

143.60

-42.84%

–

72219.22

-46.84%

–

154.30

-26.86%

–

Table 2. China 12-month summary (Day-ahead on the left; Real-time on the right). For each metric: Val is the raw score;

\Delta

LGBM is the improvement vs LGBM (ic27);

\Delta

ZS is the improvement of FutureBoosting vs its corresponding zero-shot TSFM.

Method

FR_24

DE_24

MSE

MAE

MSE

MAE

Val

\Delta

Linear

\Delta

Val

\Delta

Linear

\Delta

Val

\Delta

Linear

\Delta

Val

\Delta

Linear

\Delta

Linear

22.33

0.00%

–

2.79

0.00%

–

13.63

0.00%

–

2.55

0.00%

–

TimerXL

4.41

+80.25%

–

1.37

+50.86%

–

3.00

+77.99%

–

1.21

+52.48%

–

+ FutureBoosting

3.66

+83.61%

+16.98%

1.26

+54.81%

+7.72%

1.85

+86.43%

+38.40%

0.95

+62.69%

+21.36%

Sundial

4.00

+82.09%

–

1.29

+53.73%

–

4.23

+68.96%

–

1.42

+44.23%

–

Table 3. Real-E 24-step summary (FR on the left; DE on the right). For each metric: Val is the raw score;

\Delta

Linear is the improvement vs Regression-only Linear;

\Delta

ZS is the improvement of FutureBoosting vs its corresponding zero-shot TSFM.

Dataset	Chronos2 + Linear		Chronos2 + LGBM		Gain
	MSE	MAE	MSE	MAE	(best)
Shanxi (DA)	41165.74	128.01	34344.18	94.90	LGBM
Shanxi (RT)	50634.74	142.88	46697.19	118.93	LGBM
RealE (FR)	2.90	1.11	6.21	1.90	Linear
RealE (DE)	1.49	0.87	2.13	0.97	Linear

Table 4. Regressor choice ablation with the same TSFM backbone (Chronos2).

Figure 5. Adaptation study on Shanxi day-ahead forecasting. We compare zero-shot inference, LoRA fine-tuning, and FutureBoosting regression, with and without future-available exogenous variables.

Method	GPUs	GPU Mem (MB)	Total Time (s)
FutureBoosting	1 $\times$ 4090	11049.85	151.57
FutureBoosting (cached)	CPU only	0.00	59.24
Fine-tuning	4 $\times$ 4090	24518.00	8867.00

Table 5. Efficiency comparison on Shanxi day-ahead (per monthly window).

Figure 6. Application of FutureBoosting in Xingzhixun’s IoTDB business server.

Panel of Figure 7 — Figure 7. Sample SHAP explanations on deployed data. The TSFM-based feature derived from Chronos2 is highlighted.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Indicator	Day-ahead	Real-time
Tail ratio $p99/p50$	4.86	5.33
Extreme freq. $\mathbb{P}(p>1000)$	5.45%	5.88%
Excess kurtosis	5.05	5.39
Jump size $p99(\|\Delta p\|)$	399.8	439.9
Jump freq. $\mathbb{P}(\|\Delta p\|>200)$	2.92%	3.33%
Drift (KS ${}_{\text{max}}$ , m/m $-$ 1)	0.477	0.487

Appendix

Table 6. Key difficulty indicators of Shanxi electricity prices in 2025. Higher values indicate more challenging dynamics.

Category	Variables
Market tightness & constructed trading factors	thermal_auction_space, thermal_auction_space_st, renewable_ratio_load, renewable_ratio_power
System operation & interconnection plans	system_load_forecast, day_ahead_interconnection_plan_total, non_market_unit_output, transmission_available_capacity_yanhuai
Renewable / generation forecasts	forecast_total_power, forecast_wind_power, forecast_pv_power, forecast_new_energy_total
Calendar variables	month, weekday, day
Weather variables (summary statistics)	dew_point_2m_mean, dew_point_2m_max, dew_point_2m_min, temperature_2m_mean, temperature_2m_max, relative_humidity_2m_mean, cloud_cover_low_max, precipitation_probability_mean, extraterrestrial_ghi_mean, surface_pressure_mean, pressure_msl_mean, pressure_msl_min

Appendix

Table 7. The set of 27 future-available exogenous variables (ic27) used as direct inputs to the regressor on the Shanxi dataset.

FR	Variables (15)	DE	Variables (19)
System / load	genf_Scheduled Generation ntc_Net Position total_Day-ahead Total Load Forecast total_Actual Total Load	System / load	genf_Scheduled Generation ntc_Net Position total_Actual Total Load
Fuel-type generation	Biomass – Actual Aggregated Fossil Gas – Actual Aggregated Fossil Hard coal – Actual Aggregated Fossil Oil – Actual Aggregated Hydro Pumped Storage – Actual Aggregated Hydro Run-of-river and poundage – Actual Aggregated Hydro Water Reservoir – Actual Aggregated Nuclear – Actual Aggregated Solar – Actual Aggregated Waste – Actual Aggregated Wind Onshore – Actual Aggregated	Fuel-type generation	Biomass – Actual Aggregated Fossil Brown coal/Lignite – Actual Aggregated Fossil Gas – Actual Aggregated Fossil Hard coal – Actual Aggregated Fossil Oil – Actual Aggregated Geothermal – Actual Aggregated Hydro Pumped Storage – Actual Aggregated Hydro Run-of-river and poundage – Actual Aggregated Hydro Water Reservoir – Actual Aggregated Nuclear – Actual Aggregated Other renewable – Actual Aggregated Solar – Actual Aggregated Waste – Actual Aggregated Wind Offshore – Actual Aggregated Wind Onshore – Actual Aggregated Other – Actual Aggregated

Appendix

Table 8. Exogenous variables used for direct regression on RealE.

Figure 8. Global SHAP explanations on the test split. The Chronos2-derived forecast feature is highlighted to distinguish TSFM-predicted drivers from other exogenous variables.

Figure 9. Global SHAP explanations on the test split. The Chronos2-derived forecast feature is highlighted to distinguish TSFM-predicted drivers from other exogenous variables.

Panel of Figure 10 — Figure 10. Additional sample SHAP explanations on deployed data. The TSFM-based feature derived from Chronos2 is highlighted.

Window	Type	TimerXL		Sundial		Chronos2 (mv)		Chronos2 (future)		TimesFM		Moirai2		TiRex
Window	Type	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
202501	ZS	96031.92	195.56	77180.33	163.32	89610.94	175.98	66888.00	159.64	73564.20	160.36	81880.01	166.92	79950.36	161.65
202501	FBR	28336.35	89.36	21958.62	84.95	18692.07	77.39	20340.07	87.74	20774.21	79.08	19424.70	80.66	20981.86	83.95
202502	ZS	134084.19	237.77	121219.58	220.57	114767.00	220.21	92523.61	211.76	126918.32	213.88	123831.87	222.76	121434.01	210.61
202502	FBR	40757.15	110.22	45136.53	123.09	44370.32	120.87	48430.27	125.53	44246.05	116.91	48259.19	119.29	43017.85	118.11
202503	ZS	93755.35	196.24	80372.27	185.39	78314.09	172.93	66959.59	161.66	97939.16	180.96	90217.22	173.04	95215.36	165.77

Appendix

Table 9. Shanxi Day-Ahead 12-month window-wise results comparing zero-shot (ZS) TSFM-only forecasts and their corresponding FutureBoosting (FBR).

Window	Type	TimerXL		Sundial		Chronos2 (mv)		Chronos2 (future)		TimesFM		Moirai2		TiRex
Window	Type	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
202501	ZS	118895.21	217.91	97693.37	190.56	114730.62	199.96	99201.90	195.49	98345.31	188.98	114230.96	202.83	114310.87	198.35
202501	FBR	23393.77	100.68	27793.07	107.87	28962.75	108.12	41628.91	127.75	31895.88	114.04	27384.44	106.69	34742.31	121.41
202502	ZS	120379.08	229.16	85619.59	181.18	90050.68	203.80	80630.58	209.08	98546.03	191.38	117523.33	222.87	97648.07	179.53
202502	FBR	32541.10	119.51	36259.24	126.50	38276.06	124.70	37569.89	123.42	32796.34	116.31	35840.88	115.25	38160.78	117.90
202503	ZS	107854.53	206.39	95016.02	202.85	88038.66	191.04	77018.86	187.73	111121.30	196.46	102835.81	195.97	109298.64	178.06

Appendix

Table 10. Shanxi Real-time 12-month window-wise results comparing zero-shot (ZS) TSFM-only forecasts and their corresponding FutureBoosting (FBR).

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