A Multi-Quantile Regression Time Series Model with Interquantile Lipschitz Regularization for Wind Power Probabilistic Forecasting
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Producing probabilistic forecasts for renewable generation (RG) has become an important topic in power systems applications. This is due to the significant growth of RG participation in power systems worldwide. Additionally, it is well-known that decision making under uncertainty generally benefits from stochastic aware models, specially those relying on non symmetric costs and risk-averse assessments. Therefore, objective of this work is to propose an adaptive non-parametric time-series model driven by a regularized multiple-quantile-regression (MQR) framework. The goal is to derive a dynamic model for the conditional distribution function (CDF) describing renewable generation time series. To accomplish that, the quantile space is discretized within a user-defined granularity and an interpolation method is used to derive the full predictive CDF. Instead of estimating each quantile model separately, all models are jointly estimated through a single linear optimization problem. Thus, the estimation process converges to the global optimal parameters in polynomial time. Parsimony is imposed to the coefficient estimates across quantiles and covariates. An innovative feature of our work is the consideration of a penalization term based on a Lipschitz regularization of the first derivative of coefficients in the quantile space. The proposed regularization imposes a smooth 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.
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