Finite-sample quantiles of the Jarque–Bera test

Abstract

The finite-sample null distribution of the Jarque–Bera Lagrange multiplier test for normality differs considerably from the asymptotic χ²(2). However, asymptotic critical values are commonly used in applied work, even for relatively small sample sizes. Here, very accurate response surface approximations are developed for the 10% and 5% critical values of the test, which enable correct practical implementation.

Acknowledgments

Numerical results were derived using GAUSS and E–Views. The author is solely responsible for information communicated, and Electrabel SA is not responsible for any views or results expressed.

Notes

Response surfaces are numerical-analytical approximations, that have been widely applied in econometrics; e.g., Ericsson (1991), Cheung and Lai (1995), MacKinnon (1994), MacKinnon et al. (1999), and Ericsson and MacKinnon (2002).