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Journal of Financial Econometrics Advance Access originally published online on January 16, 2008
Journal of Financial Econometrics 2008 6(2):271-289; doi:10.1093/jjfinec/nbm023
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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Detecting ARCH Effects in Non-Gaussian Time Series

Burkhard Raunig
     Oesterreichische Nationalbank

Address correspondence to: Oesterreichische Nationalbank, Economic Studies Division, Otto-Wagner-Platz 3, POB 61, A-1011 Vienna, Austria, or e-mail: burkhard.raunig{at}oenb.co.at

JEL Classification: C12, C14, C22, C52


  Abstract

Engles ARCH test has become the standard test for ARCH effects in applied work. Under non-normality the true rejection probability of this test can differ substantially from the nominal level, however. Bootstrap and Monte Carlo versions of the test may then be used instead. This paper proposes an alternative test procedure. The new test exploits the empirical distribution of the data and an extended probability integral transformation. The test is compared with the former tests in Monte Carlo experiments. Under normality, the new test works as well as the conventional Monte Carlo test and the bootstrap. Under non-normality, the test tends to be more accurate and more powerful than the bootstrapped ARCH test. The procedure is then used to test for ARCH effects in S&P 500 returns sampled at different frequencies. In contrast to the standard and the bootstrapped ARCH tests, the new test detects ARCH effects in the transformed low-frequency returns.

KEYWORDS: ARCH, GARCH, bootstrap, Monte Carlo tests, distributional assumptions

The opinions expressed herein do not necessarily reflect those of the Oesterreichische Nationalbank. I would like to thank the editor, an associate editor, and the anonymous referees. Their comments and suggestions greatly helped to improve the paper.

Received August 23, 2004; revised September 19, 2007; accepted November 20, 2007


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