The joint asymptotic distribution of the sample sequential coefficients of skewness and kurtosis is obtained without assuming that the data is drawn from a normal population. Nonparametric tests are developed for testing against a change in the value of the skewness and kurtosis coefficients. Tests for a change from a given distribution are also developed.

change point tests, goodness-of-fit tests, nonparametric tests, strong approximations, Wiener processes.