Afrika Statistika

On change-point detection in volatile series using GARCH models

Edoh Katchekpele, Kossi Essona Gneyou, and Abdou Kâ Diongue

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Abstract

We study a Cumulative Sum (CUSUM)-type test to detect a change in the unconditional variance of GARCH models. We show that, under the null hypothesis (no change), the CUSUM test statistic converges to the supremum of a standard Brownian bridge. Using Monte Carlo simulation, we demonstrate that the asymptotic power of the test is almost the unity and compare the test result with existing results in the literature. Finally, the test procedure is applied to real-world situation namely the Standard and Poor (S&P) 500 stock market returns (09/16/1980 to 01/31/2008) where we are able to detect a change in the unconditional variance at a very early stage of the financial crisis in comparison to other previous analyses of the same dataset.

Résumé

Nous étudions un test de type CUSUM pour la détection de rupture dans la variance inconditionnelle des modèles GARCH. Nous montrons que sous l'hypothèse nulle, notre statistique de test converge vers le supremum d'un pont Brownien standard. Utilisant des simulations de type Monte Carlo, nous démontrons que la puissance asymptotique du test est presqu'égale à l'unité et comparons le résultat du test avec les résultats existants dans la littérature. Enfin, un exemple d'application sur les données réelles des rendements du marché boursier S&P (Standard and Poor) 500 (16/09/1980 au 31/01/2008) nous a permis de détecter une rupture dans la variance inconditionnelle à un stade très précoce de la crise financière par rapport à d'autres analyses précédentes du même ensemble de données.

Article information

Source
Afr. Stat., Volume 12, Number 2 (2017), 1333-1346.

Dates
Received: 2 June 2017
Accepted: 8 July 2017
First available in Project Euclid: 14 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.as/1505354427

Digital Object Identifier
doi:10.16929/as/2017.1333.107

Mathematical Reviews number (MathSciNet)
MR3703443

Zentralblatt MATH identifier
1373.62428

Subjects
Primary: 37M10: Time series analysis 62F03: Hypothesis testing 62F05: Asymptotic properties of tests

Keywords
GARCH model Change-point Squared cusum test Brownian bridge Weak convergence

Citation

Katchekpele, Edoh; Gneyou, Kossi Essona; Diongue, Abdou Kâ. On change-point detection in volatile series using GARCH models. Afr. Stat. 12 (2017), no. 2, 1333--1346. doi:10.16929/as/2017.1333.107. https://projecteuclid.org/euclid.as/1505354427


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