Predictive Uncertainty in Short-Term PV Forecasting under Missing Data: A Multiple Imputation Approach

Parastoo Pashmchi; Jérôme Benoit; Motonobu Kanagawa

cs.LGMar 16, 2026

Predictive Uncertainty in Short-Term PV Forecasting under Missing Data: A Multiple Imputation Approach

Authors: Parastoo Pashmchi, Jérôme Benoit, Motonobu Kanagawa

Organizations: SAP Labs France, Mougins, France · EURECOM, Biot, France

Abstract

Missing values are common in photovoltaic (PV) power data, yet the uncertainty they induce is not propagated into predictive distributions. We develop a framework that incorporates missing-data uncertainty into short-term PV forecasting by combining stochastic multiple imputation with Rubin's rule. The approach is model-agnostic and can be integrated with standard machine-learning predictors. Empirical results show that ignoring missing-data uncertainty leads to overly narrow prediction intervals. Accounting for this uncertainty improves interval calibration while maintaining comparable point prediction accuracy. These results demonstrate the importance of propagating imputation uncertainty in data-driven PV forecasting.

Figures & tables

Fig. 1 : Example of missing observations in real PV power measurements collected at EURECOM, illustrating complete-day gaps and prolonged zero-output periods consistent with system outages or failures.

Fig. 2 : Comparison of single and multiple imputation for one-hour-ahead prediction with a Random Forest model. The shaded regions show the 95% prediction intervals. Single imputation gives overly narrow intervals, whereas the proposed multiple-imputation approach accounts for missing-value uncertainty and gives wider intervals.

Panel of Figure 3 — Fig. 3 : Dataset from the EU GRIDouble project used in our experiments. Top: original hourly DC power. Middle: DC power after block-wise removal of several contiguous weeks (29.5% missing). Bottom: corresponding hourly irradiation (GHI).

Imputation Setup	$B$	RF	kNN	MLP	Lasso
1) SI train, SI test	–	74.4	83.8	83.0	85.1
2) SI train, MI test	5	84.1	88.5	90.0	90.7
	10	83.9	88.1	90.5	91.5
3) MI train, MI test	5	85.2	92.1	93.1	93.4
	10	84.5	92.1	93.6	92.8

TABLE I : Coverage probability (%) of 95% prediction intervals under the normal distribution

Imputation Setup	$B$	RF	kNN	MLP	Lasso
1) SI train, SI test	–	70.7	78.8	72.1	70.1
2) SI train, MI test	5	80.7	83.1	78.7	77.0
	10	80.9	83.6	79.5	76.5
3) MI train, MI test	5	83.7	88.1	78.3	79.5
	10	82.9	88.7	84.7	79.2

TABLE II : Coverage probability (%) of 95% prediction intervals under the gamma distribution

Imputation Setup	$B$	RF	kNN	MLP	Lasso
1) SI train, SI test	–	0.123	0.131	0.124	0.132
2) SI train, MI test	5	0.127	0.136	0.126	0.132
	10	0.126	0.132	0.123	0.129
3) MI train, MI test	5	0.127	0.136	0.125	0.132
	10	0.126	0.133	0.121	0.130

TABLE III : NRMSE for different algorithms under each imputation setup

Panel of Figure 7 — Fig. 4 : 95% prediction intervals ( $B=5$ ) for Random Forest under (a) gamma and (b) normal predictive distributions, shown for three imputation setups: (1) SI train & test, (2) SI train with MI test, and (3) MI train & test. Black thick curve: ground truth; thick colored curve: predictive means; shaded region: 95% prediction intervals.

Panel of Figure 8 — Fig. 5 : 95% prediction intervals ( $B=5$ ) for MLP under (a) gamma and (b) normal predictive distributions, shown for three imputation setups: (1) SI train & test, (2) SI train with MI test, and (3) MI train & test. Black thick curve: ground truth; thick colored curve: predictive means; shaded region: 95% prediction intervals.

Panel of Figure 9 — Fig. 6 : 95% prediction intervals ( $B=5$ ) for Lasso under (a) gamma and (b) normal predictive distributions, shown for three imputation setups: (1) SI train & test, (2) SI train with MI test, and (3) MI train & test. Black thick curve: ground truth; thick colored curve: predictive means; shaded region: 95% prediction intervals.

Panel of Figure 10 — Fig. 7 : 95% prediction intervals ( $B=5$ ) for kNN under (a) gamma and (b) normal predictive distributions, shown for three imputation setups: (1) SI train & test, (2) SI train with MI test, and (3) MI train & test. Black thick curve: ground truth; thick colored curve: predictive means; shaded region: 95% prediction intervals.

Jérôme Benoit received the Engineer’s degree in computer science from Polytech’Marseille, Marseille, France, in 2019. He previously received the M.Sc. degree in mathematics from Aix-Marseille Université, Marseille, France, in 1997. He has been working as an R&D Software Engineer at SAP Labs France since 2019. His research focuses on e-mobility, electric vehicle charging infrastructure, and machine learning applied to smart charging systems.

Table 12

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Solar power forecasting predicts photovoltaic generation and irradiance from weather, imagery, plant data, and recent output to support reliable grid and energy decisions.

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Solar photovoltaic (PV) forecasting in regions affected by load shedding is challenging because reliable historical observations are scarce. This study proposes a transfer learning framework combined with Conformalized Quantile Regression (CQR) to improve PV power forecasting and provide reliable uncertainty estimates under severe data scarcity. A source-domain PV dataset from Alice Springs, Australia, is used to pretrain a temporal forecasting model, which is then adapted to simulated Bangladesh PV data representing different levels of historical availability. Experimental results show that transfer learning reduces RMSE by up to 23.7% when only one month of target-domain data is available and by 13.7% with three months of data. The proposed Transfer Learning plus CQR framework achieves 94.3% empirical coverage with three months of target data while producing prediction intervals that are 14% narrower than those obtained without transfer learning. These results demonstrate that combining transfer learning with conformal uncertainty quantification can improve both point forecasting accuracy and uncertainty reliability when target-domain PV data are severely limited.

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