Dynamic Modelling of Heavy-Tailed Cylindrical Time Series

A dynamic modelling for heavy-tailed cylindrical time series is developed by combining score-driven models with a generalised Pareto-type cylindrical distribution. The proposed specification extends existing cylindrical models by allowing location, scale, concentration, andcrucially, the tail index of the linear component through the conditional distribution of speed to vary according to its score. Whereas the Weibull-von Mises model, whose linear componentexhibits exponentially decaying tails, the GPar specification admits polynomial tail decay. An explicit expression for the time-varying circular-linear dependence measure is also derived. The methodology is applied to high-frequency data from two onshore wind turbines in Germany. The empirical results indicate that allowing time-varying tail thickness leads to overall improvements compared to the Weibull-von Mises model. The proposedmodelprovidesaflexibleandcomputationallytractableframeworkforanalysing heavy-tailed cylindrical time series in environmental and energy applications.