A note on testing for skewness persistence

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