Probabilistic wind power forecasting resilient to missing values: an adaptive quantile regression approach

TL;DR

This paper addresses the challenge of probabilistic wind power forecasting when data contain missing values. It proposes an adaptive quantile regression framework with two modules: a feature extraction block whose biases adapt to missingness patterns and a non-crossing quantile regression network that enforces monotonicity across quantiles. The method works across all missingness mechanisms (MCAR/MAR/MNAR) and does not require data preprocessing such as imputation, achieving state-of-the-art CRPS in case studies while maintaining computational practicality. The approach offers robustness to missing data and practical benefits for wind power forecasting in industrial settings, with potential extensions to time-varying parameters and adaptive weights.

Abstract

Probabilistic wind power forecasting approaches have significantly advanced in recent decades. However, forecasters often assume data completeness and overlook the challenge of missing values resulting from sensor failures, network congestion, etc. Traditionally, this issue is addressed during the data preprocessing procedure using methods such as deletion and imputation. Nevertheless, these ad-hoc methods pose challenges to probabilistic wind power forecasting at both parameter estimation and operational forecasting stages. In this paper, we propose a resilient probabilistic forecasting approach that smoothly adapts to missingness patterns without requiring preprocessing or retraining. Specifically, we design an adaptive quantile regression model with parameters capable of adapting to missing patterns, comprising two modules. The first is a feature extraction module where weights are kept static and biases are designed as a function of missingness patterns. The second is a non-crossing quantile neural network module, ensuring monotonicity of quantiles, with higher quantiles derived by adding non-negative amounts to lower quantiles. The proposed approach is applicable to cases under all missingness mechanisms including missing-not-at-random cases. Case studies demonstrate that our proposed approach achieves state-of-the-art results in terms of the continuous ranked probability score, with acceptable computational cost.

Figures (9)

• Figure 1: Illustration for samples classification according to missingness patterns.
• Figure 2: The sketch of the proposed approach, where blank blocks in $\Tilde{\boldsymbol{x}}_t$ indicate missing values.
• Figure 3: The structure of feature extraction block.
• Figure 4: Illustration of two kinds of missingness cased by the MCAR mechanism, namely (a) sporadic missingness (b)block-wise missingness, where grey blocks indicate observations and white blocks indicate missingness.
• Figure 5: 1-step ahead 90% prediction intervals by the proposed model for 144 successive observations in case 1.