Large-scale streaming data are common in modern machine learning applications and have led to the development of online learning algorithms. Many fields, such as supply chain management, weather and meteorology, energy markets, and finance, have pivoted towards using probabilistic forecasts, which yields the need not only for accurate learning of the expected value but also for learning the conditional heteroskedasticity. Against this backdrop, we present a methodology for online estimation of regularized linear distributional models for conditional heteroskedasticity. The proposed algorithm is based on a combination of recent developments for the online estimation of LASSO models and the well-known GAMLSS framework. We provide a case study on day-ahead electricity price forecasting, in which we show the competitive performance of the adaptive estimation combined with strongly reduced computational effort. Our algorithms are implemented in a computationally efficient Python package.

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