A Multi-Quantile Regression Time Series Model with Interquantile Lipschitz Regularization for Wind Power Probabilistic Forecasting

Abstract: Modern decision-making processes require uncertainty-aware models, especially those relying on non-symmetric costs and risk-averse profiles. The objective of this work is to propose a dynamic model for the conditional non-parametric distribution function (CDF) to generate probabilistic forecasts for a renewable generation time series. To do that, we propose an adaptive non-parametric time-series model driven by a regularized multiple-quantile-regression (MQR) framework. In our approach, all regression models are jointly estimated through a single linear optimization problem that finds the global-optimal parameters in polynomial time. An innovative feature of our work is the consideration of a Lipschitz regularization of the first derivative of coefficients in the quantile space, which imposes coefficient smoothness. The proposed regularization induces a coupling effect among quantiles creating a single non-parametric CDF model with improved out-of-sample performance. A case study with realistic wind-power generation data from the Brazilian system shows: 1) the regularization model is capable to improve the performance of MQR probabilistic forecasts, and 2) our MQR model outperforms five relevant benchmarks: two based on the MQR framework, and three based on parametric models, namely, SARIMA, and GAS with Beta and Weibull CDF.