A measure of information and its applications to test for randomness against ARMA alternatives and to goodness-of-fit test

In this paper we introduce a new method for the problem of testing for randomness against the alternative of ARMA dependence. We give the asymptotic law of our statistic under the null hypothesis and under the alternative hypothesis. Our method is based on a new measure of information between two stationary stochastic processes. As an application, we also derive a test for a simple hypothesis in the autoregressive case and in the ARMA case.