This paper shows that the tests of skewness persistence considered by
Muralidhar (1993) far exceed the true Type I error. That is, the proba
bilities of detecting an increase (decrease) in skewness from one time
period to another when in fact there is no change are inflated. Conse
quently, the higher power achieved by these tests comes at the cost of
a higher than specified level of Type I error. We propose a new test
which maintains the specified Type I error levels. Additionally, the p
ower of this test for lognormal distributions is reported.