A test for multivariate ARCH effects

• Published in: Applied economics letters Vol. 12; no. 7; pp. 411 - 417
• Main Authors: Scott Hacker, R., Hatemi-J, Abdulnasser
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis Group 10.06.2005; Taylor and Francis Journals; Taylor & Francis LLC
• Series: Applied Economics Letters
• Subjects: Applied economics; ARCH; bootstrap; Bootstrap mechanism; Bootstrap method; Business and economics; Econometric models; Econometrics; Economic analysis; Economic models; Economic theory; Economics; Ekonometri; Ekonomi; Humaniora-samhällsvetenskap; Humanities and Social sciences; LM test; Matematik; Mathematics; Model testing; multivariate; Multivariate analysis; Nationalekonomi; Natural Sciences; Naturvetenskap; Probability Theory and Statistics; SAMHÄLLSVETENSKAP; Sannolikhetsteori och statistik; SOCIAL SCIENCES; Statistical models; Studies; VAR; Vector autoregressive models
• ISSN: 1350-4851; 1466-4291; 1466-4291
• DOI: 10.1080/13504850500092129

This paper extends Engle's LM test for ARCH affects to multivariate cases. The size and power properties of this multivariate test for ARCH effects in VAR models are investigated based on asymptotic and bootstrap distributions. Using the asymptotic distribution, deviations of actual size from nominal size do not appear to be very excessive. Nevertheless, there is a tendency for the actual size to overreject the null hypothesis when the nominal size is 1% and underreject the null when the nominal size is 5% or 10%. It is found that using a bootstrap distribution for the multivariate LM test is generally superior in achieving the appropriate size to using the asymptotic distribution when (1) the nominal size is 5%; (2) the sample size is small (40 observations) and/or the VAR system is stable. With a small sample, the power of the test using the bootstrap distribution also appears better at the 5% nominal size.