We study a circular-circular multiplicative regression model, characterized by an angular error distribution assumed to be wrapped Cauchy. We propose a specification procedure for this model, focusing on adapting a recently proposed goodness-of-fit test for circular distributions. We derive its limiting properties and study the power performance of the test through extensive simulations, including the adaptation of some other well-known goodness-of-fit tests for this type of data. To emphasize the practical relevance of our methodology, we apply it to several small real-world datasets and wind direction measurements in the Black Forest region of southwestern Germany, demonstrating the power and versatility of the presented approach.

翻译：我们研究一种圆-圆乘法回归模型，其特征是假设角误差分布为包裹柯西分布。我们提出了针对该模型的设定检验程序，重点在于调整一种最近提出的圆分布拟合优度检验方法。我们推导了其极限性质，并通过大量模拟研究了该检验的功效表现，其中包括针对此类数据调整其他几种著名的拟合优度检验方法。为强调我们方法的实际意义，我们将其应用于若干小型真实数据集以及德国西南部黑森林地区的风向测量数据，展示了所提出方法的功效与普适性。