Distribution-Free test for Changepoint Detection in Angular Mean Direction: Application in Finance

2026-08-08

AI Summary

This study addresses the lack of distribution-free methods for change-point detection in the mean direction of circular data by proposing, for the first time, a framework grounded in the intrinsic geometry of the torus that requires no distributional assumptions. The approach quantifies uncertainty using angular squared distance to construct a test statistic and rigorously establishes its asymptotic Kolmogorov distribution under the null hypothesis, along with the consistency of the estimator under the alternative. Simulation studies demonstrate superior performance compared to existing methods such as those based on circular arc-length distance. When applied to timestamps of extreme price events in Bitcoin, Ethereum, and gold—modeled as circular data—the method successfully identifies statistically significant change points.

Abstract

In this paper, we propose a distribution-free test for detecting changepoint in the mean direction of angular data. The uncertainty in angular measurements is quantified through the \textit{square of an angle}, derived from the intrinsic geometry of the torus. It is established that, under the null hypothesis, the test statistic distributionally converges to the Kolmogorov distribution, while under the alternative hypothesis, both the consistency of the test and the asymptotic properties of the changepoint estimator are established. Through extensive simulations, we compare the empirical performance of the proposed method with two existing approaches for angular data and further benchmark it against a test based on the circular arc length distance. Finally, we demonstrate the practical utility of our approach by analyzing the timestamps of extreme events in Bitcoin, Ethereum, and Gold price datasets, where the continuous, high-frequency nature of the data is modeled in the circular framework.

Problem

• changepoint detection
• angular data
• mean direction
• distribution-free test
• circular statistics

Innovation

• distribution-free
• changepoint detection
• angular data
• mean direction
• circular statistics