The investigation modes, are carried under three angles:epistemological, statistical and economical approaches. In the first part of the thesis, we specify, in an epistemological approach, in what the concept of long-memory can appear, as a new kühnian ''paradigm'' for macroeconomics and finance. In the second part of the thesis, we propose, in a semiparametric statistical approach, three extensions of the most elaborate IR (Increment Ratio) statistics of Surgailis et al, (2008). First, a multidimensional central limit theorem is established, for a vector made up of several IR statistics. Second, a chi2 goodness of fit test is deduced from this Multidimensional central limit theorem. Lastly, this Multidimensional central limit theorem allowed us to build adaptive versions of the estimator and the goodness of fit test, studied within a general semiparametric framework. We prove that the adaptive estimator of the long memory parameter follows an Oracle property. Simulations which we carried out attest of the precision and the robustness of the estimator and the goodness of fit test, even in the non Gaussian case. In the third part of the thesis, we deduce from our adaptive Multidimensional Increment Ratio statistics, two tests respectively of stationarity and nonstationarity, for any stationary or nonstationary I(d) process, and for any real number d such that -0.5< d < 1.25. In an empirical econometric approach, we implement these previous theoretical results, and compare them with those resulting from other statistical methods: parametric, semiparametric or nonparametric (or heuristic) applied to economical and financial series.
