  We revisit the Kolmogorov-Smirnov and Cram\'er-von Mises goodness-of-fit
(GoF) tests and propose a generalisation to identically distributed, but
dependent univariate random variables. We show that the dependence leads to a
reduction of the "effective" number of independent observations. The
generalised GoF tests are not distribution-free but rather depend on all the
lagged bivariate copulas. These objects, that we call "self-copulas", encode
all the non-linear temporal dependences. We introduce a specific, log-normal
model for these self-copulas, for which a number of analytical results are
derived. An application to financial time series is provided. As is well known,
the dependence is to be long-ranged in this case, a finding that we confirm
using self-copulas. As a consequence, the acceptance rates for GoF tests are
substantially higher than if the returns were iid random variables.
