  We suggest a new approach to hypothesis testing for ergodic and stationary
processes. In contrast to standard methods, the suggested approach gives a
possibility to make tests, based on any lossless data compression method even
if the distribution law of the codeword lengths is not known. We apply this
approach to the following four problems: goodness-of-fit testing (or identity
testing), testing for independence, testing of serial independence and
homogeneity testing and suggest nonparametric statistical tests for these
problems. It is important to note that practically used so-called archivers can
be used for suggested testing.
