Specification tests for error distribution in regression models with a directional response variable

Abstract

Recently, interest in circular regression analysis has been growing across diverse domains such as medicine, meteorology, economy, geography, etc. Although there are many such models proposed so far, the diagnostic tests for testing error assumptions have not been explored yet. We aim to fill this gap by proposing a novel approach for testing error distribution in multiplicative regression models. In particular, we adapted several classes of goodness-of-fit tests proposed for iid circular data and explored their properties. As an example of the novel approach, we present results, including limiting properties of test statistics and the summary of a wide empirical study, for the circular-circular regression model proposed by Kato (2010). The model is characterized by a regression curve formulated through a Möbius transformation and an angular error distribution assumed to follow a wrapped Cauchy distribution. To emphasize the practical relevance of our methodology, we apply it to multiple real-world datasets, demonstrating the significance and versatility of the presented approach.