In this paper we consider the problem of comparison of two strictly stationary processes. The novelty of our approach is that we consider all their d-dimensional joint distributions, for . Our procedure consists in expanding their densities in a multivariate orthogonal basis and comparing their k first coefficients. The dimension d to consider and the number k of coefficients to compare in view of performing the test can growth with the sample size and are automatically selected by a two-step data-driven procedure. The method works for possibly paired, short or long range dependent processes. A simulation study shows the good behavior of the test procedure. In particular, we apply our method to compare ARFIMA processes. Some real-life applications also illustrate this approach.