On the application of Jammalamadaka-Jim\'enez Gamero-Meintanis test for circular regression model assessment

TL;DR

This paper evaluates a goodness-of-fit test for circular regression models with wrapped Cauchy errors, demonstrating its effectiveness through simulations and real-world wind data analysis.

Contribution

It adapts a recent circular distribution goodness-of-fit test for circular regression models and assesses its theoretical properties and practical performance.

Findings

The test has good power in simulations.

It successfully analyzes wind direction data.

The methodology is versatile for real-world applications.

Abstract

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.