  In this paper the testing of normality for unconditionally heteroscedastic
macroeconomic time series is studied. It is underlined that the classical
Jarque-Bera test (JB hereafter) for normality is inadequate in our framework.
On the other hand it is found that the approach which consists in correcting
the heteroscedasticity by kernel smoothing for testing normality is justified
asymptotically. Nevertheless it appears from Monte Carlo experiments that such
methodology can noticeably suffer from size distortion for samples that are
typical for macroeconomic variables. As a consequence a parametric bootstrap
methodology for correcting the problem is proposed. The innovations
distribution of a set of inflation measures for the U.S., Korea and Australia
are analyzed.
