  This paper is first devoted to study an adaptive wavelet based estimator of
the long memory parameter for linear processes in a general semi-parametric
frame. This is an extension of Bardet {\it et al.} (2008) which only concerned
Gaussian processes. Moreover, the definition of the long memory parameter
estimator is modified and asymptotic results are improved even in the Gaussian
case. Finally an adaptive goodness-of-fit test is also built and easy to be
employed: it is a chi-square type test. Simulations confirm the interesting
properties of consistency and robustness of the adaptive estimator and test.
