  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.
