  This article proposes a class of goodness-of-fit tests for the
autocorrelation function of a time series process, including those exhibiting
long-range dependence. Test statistics for composite hypotheses are functionals
of a (approximated) martingale transformation of the Bartlett $T_p$-process
with estimated parameters, which converges in distribution to the standard
Brownian motion under the null hypothesis. We discuss tests of different
natures such as omnibus, directional and Portmanteau-type tests. A Monte Carlo
study illustrates the performance of the different tests in practice.
