Unveiling change-point detection with ARMA-GARCH models

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Edoh Katchekpele
Issa Cherif Geraldo
Tchilabalo Abozou Kpanzou

Abstract

This paper delves into the asymptotic theory of a Cumulative Sum (CUSUM)-type test designed for detecting change points in the variance of AutoRegressive Moving-Average models, incorporating Generalized Autoregressive Conditional Heteroscedasticity innovations. We demonstrate that, under the null hypothesis (no change), the CUSUM test statistic converges to the supremum of a standard Brownian bridge. Using a Monte Carlo simulation, we highlight the strong performance of our proposed test when compared to the methods by Song and Kang. Furthermore, we provide a real-world data analysis to showcase the practical application of our test.

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How to Cite
Katchekpele, E., Geraldo, I. C., & Kpanzou, T. A. (2024). Unveiling change-point detection with ARMA-GARCH models. Gulf Journal of Mathematics, 17(2), 226-242. https://doi.org/10.56947/gjom.v17i2.2131
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