A new test for whiteness

We consider the problem of testing whiteness, i.e., to say whether or not a given sequence of data is not correlated (i.i.d if Gaussian). This information could be of help when one is interested in the adequacy of a chosen model that is assumed to fit a set of data. We first introduce a new parameter or, more precisely, a "distance" to whiteness and then construct the new test for whiteness. We derive its distributions under both hypotheses: the null hypothesis (whiteness) and the non-null one. We provide the power of our new test and compare it empirically with the Portmanteau and Fisher test. Several numerical experiments are carried out in order to emphasize the performances of our new statistic for whiteness.