Finite and asymptotic properties of a nonparametric test for randomness against serial dependence

A very important problem in time series analysis is testing for randomness against serial dependence. Classical parametric methods, commonly based on the autocorrelation coefficient, can be misleading when the underlying distributional assumptions are not fulfilled. In this paper the use of a nonparametric measure of serial dependence, based on Gini's cograduation index, is discussed. More specifically, the finite and asymptotic properties of this test-statistic are discussed; the test is then compared with its competitors via asymptotic relative efficiency.