  The increment ratio (IR) statistic was first defined and studied in Surgailis
{\it et al.} (2007) for estimating the memory parameter either of a stationary
or an increment stationary Gaussian process. Here three extensions are proposed
in the case of stationary processes. Firstly, a multidimensional central limit
theorem is established for a vector composed by several IR statistics.
Secondly, a goodness-of-fit $\chi^2$-type test can be deduced from this
theorem. Finally, this theorem allows to construct adaptive versions of the
estimator and test which are studied in a general semiparametric frame. The
adaptive estimator of the long-memory parameter is proved to follow an oracle
property. Simulations attest of the interesting accuracies and robustness of
the estimator and test, even in the non Gaussian case.
