This study develops a data-driven framework that integrates Functional Data Analysis (FDA) with Seasonal-Trend decomposition using Loess (STL) to investigate how energy production dynamics interact with electricity prices in Germany and China: two contrasting markets governed by marginal cost pricing and policy-anchored regimes, respectively. By decomposing time series into trend-cycle-residual components, we isolate long-term structural forces from short-term variability and policy-induced distortions. Functional Principal Component Analysis (FPCA) reveals nation-specific modes: fossil fuels in Germany and nuclear energy in China function as flexible stabilizers, mitigating renewable intermittency within their respective pricing architectures. Multivariate Functional Response Analysis(MFRA) further quantifies time-varying elasticity coefficients, revealing that Germany’s liberalized market structure amplifies the coupling between renewable generation and electricity prices, whereas China’s coal-indexed benchmark pricing dampens this linkage. In Germany, where excess renewable capacity during critical periods, particularly summer photovoltaic surpluses, paradoxically increases overall system costs, highlighting the need for investments in grid flexibility rather than continued unilateral capacity expansion. Conversely, China’s hybrid system exhibits that although wind and solar technologies achieve rapid cost reductions, rigid pricing mechanisms for hydropower and nuclear energy distort market signals, inadvertently sustaining fossil gas’s marginal pricing influence. Finally, prediction results validate the robustness of the estimated coefficient functions.

Wind energy plays a crucial role in the transition to green energy. Although wind turbine technology continues to improve and repowering takes place, maintenance costs for wind turbines remain a major issue. Horizontal-axis wind turbines with azimuth engines adjust the nacelle and blades to the wind direction to maximize energy capture. However, frequent directional changes despite motion reversals can cause significant cable damage over time.

In this paper, we extend regime-switching models for circular variables by incorporating seasonality and allowing for more than two regimes in the joint distribution of wind direction and wind speed. The model is built on a dynamic mixture framework with score-driven updates, where regime probabilities are determined via a softmax transformation of latent variables. By explicitly modelling the joint density across multiple regimes, the approach captures switching behaviour and seasonal effects.

Using high-frequency data coming from wind farms located in two different wind zones in Germany, we test our approach and demonstrate its ability to forecast regime switches in wind direction. Our model offers wind farm operators a practical tool to optimize nacelle adjustment strategies, for example during summer months with frequent directional shifts and lower wind speeds. This has the potential not only to reduce maintenance costs but also to improve competitiveness in spot market trading. While we focus on wind energy applications, the approach is general and can be applied to other contexts, such as modelling pollutant dispersion in the atmosphere.

We consider a general high-dimensional VAR setup that covers periodic or panel VARs, among others. The high-dimensionality of these models causes considerable problems when estimating them with standard methods such as OLS. Therefore we propose the use of appropriate regularization methods such as the fused lasso to control the dimension of the models. The fused lasso combines the standard lasso penalty term with a fusion penalty term. While the lasso penalty shrinks parameter estimates towards zero, the fusion penalty is designed to shrink two parameter estimates towards each other. Accordingly, the application of the fused lasso is particularly suitable in periodic VAR applications with sparse periodic structures or in panel VAR applications with similar cross-sectional dependence structures. We consider estimation and inference in general high-dimensional VAR setups using the fused lasso. Further, we provide a method for suitable choices of the tuning parameters that also accounts for the dependencies in the data. A key result of the paper is to provide valid inference on many target parameter in high-dimensional VARs. For this purpose, we use the asymptotic properties of desparsified variants of the regularized estimators with fused lasso. Finally, we demonstrate the practical usefulness of our approach by a real data application and illustrate its performance via Monte Carlo simulations.

Forecast reconciliation is applied to ensure that forecasts for multiple time series on different levels of a hierarchy conform to the linear restrictions prescribed by the hierarchy. When reconciling probabilistic forecasts, this linear restriction is to be enforced on the distributional level. Building upon the approach of Panagiotelis et al. (European Journal of Operational Research, 306(2):693–706, 2023), who construct their reconciled forecasts as a linear function of the base-level forecasts, we construct the reconciled forecasts using a feedforward multilayer perceptron (MLP) neural network. One aim of our work is to study under which circumstances a linear reconciliation strategy is sufficient (and optimal) and when non-linear generalizations, such as the MLP, are needed. As an empirical application, the different reconciliation strategies are compared when applied to probabilistic one-step ahead forecasts for German wind-power production at three different spatial hierarchical levels.