Although circular data occur in a wide range of scientific fields, the methodology for distributional modelling and probabilistic forecasting of circular response variables is quite limited. Most of the existing methods are built on generalized linear and additive models, which are often challenging to optimize and interpret. Specifically, capturing abrupt changes or interactions is not straightforward but often relevant, e.g. for modelling wind directions subject to different wind regimes. Additionally, automatic covariate selection is desirable when many predictor variables are available, as is often the case in weather forecasting. To address these challenges we suggest a general distributional approach using regression trees and random forests to obtain probabilistic forecasts for circular responses. Using trees simplifies model estimation as covariates are used only for partitioning the data and subsequently just a simple von Mises distribution is fitted in the resulting subgroups. Circular regression trees are straightforward to interpret, can capture non‐linear effects and interactions, and automatically select covariates affecting location and/or scale in the von Mises distribution. Circular random forests regularize and smooth the effects from an ensemble of trees. The new methods are applied to probabilistic wind direction forecasting at two Austrian airports, considering other common approaches as a benchmark.

中文翻译：

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循环回归树木和森林在概率风向预测中的应用

尽管循环数据出现在广泛的科学领域，但是循环响应变量的分布建模和概率预测的方法非常有限。现有的大多数方法都建立在广义线性模型和加性模型的基础上，这些模型通常难以优化和解释。具体而言，捕捉突变或相互作用并不是一件容易的事，而通常是相关的，例如对于模拟受不同风况影响的风向。另外，当许多预测变量可用时，自动协变量选择是理想的，这在天气预报中经常是这种情况。为了应对这些挑战，我们建议使用回归树和随机森林的一般分布方法来获得循环响应的概率预测。使用树简化了模型估计，因为协变量仅用于划分数据，随后仅将简单的冯·米塞斯分布拟合到所得子组中。循环回归树易于解释，可以捕获非线性效应和相互作用，并自动选择影响von Mises分布中位置和/或规模的协变量。圆形随机森林使树木合群的效果正规化和平滑。以其他常用方法为基准，将新方法应用于两个奥地利机场的概率风向预测。可以捕获非线性效应和相互作用，并自动选择影响von Mises分布中位置和/或规模的协变量。圆形随机森林使树木合群的效果正规化和平滑。以其他常用方法为基准，将新方法应用于两个奥地利机场的概率风向预测。可以捕获非线性效应和相互作用，并自动选择影响von Mises分布中位置和/或规模的协变量。圆形随机森林使树木合群的效果正规化和平滑。以其他常用方法为基准，将新方法应用于两个奥地利机场的概率风向预测。