Arc length tests for comparing the dynamics between GARCH processes

Tunno, Ferebee; Muñoz Ruiz, Javier

doi:10.2140/involve.2025.18.459

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Arc length tests for comparing the dynamics between GARCH processes

Ferebee Tunno and Javier Muñoz Ruiz

Vol. 18 (2025), No. 3, 459–471

DOI: 10.2140/involve.2025.18.459

Abstract

We present an arc length test that compares the conditional volatility structures between independent, stationary GARCH processes. A wide variety of simulations are conducted that reveal the power and error of this test to be reasonable and robust with some exceptions. An application involving the daily returns from four major penny cryptocurrencies is presented as well. The years 2020 and 2021 are considered, but since the daily closing prices in 2021 behave very differently from those in 2020, the two years are treated separately.

Keywords

conditional volatility, arc length, GARCH, cryptocurrency

Mathematical Subject Classification

Primary: 60G10

Milestones

Received: 23 June 2023

Revised: 6 January 2024

Accepted: 12 January 2024

Published: 28 April 2025

Communicated by Robert B. Lund

Authors

Ferebee Tunno
Department of Mathematics and Statistics Arkansas State University Jonesboro, AR United States

Javier Muñoz Ruiz
Department of Mathematics and Statistics Arkansas State University Jonesboro, AR United States

Vol. 18, No. 3, 2025