This study is devoted to the use of wavelets in two different fields, constructions of bases on the interval and long-memory parameter estimation. In the first part we present general constructions of orthogonal and biorthogonal multiresolution analyses on the interval. In the first one, we describe a direct method to define an orthonormal multiresolution analysis. In the second one, we use the integration and derivation method for constructing a biorthogonal multiresolution analysis. As applications, we prove that these analyses are adapted to study regular functions on the interval (H^{s}([0,1])$ et $H^{s}_{0}([0,1])$ for $s\in\mathbb{N}$). The second part is devoted to the study of adaptive wavelet-based estimators of the long-memory parameter for Gaussian then linear processes in a general semiparametric frame. We introduce and develop the choice of a data-driven optimal bandwidth. Moreover, we establish central limit theorems for the estimators of the memory parameter with the minimax rate of convergence (up to a logarithm factor). Finally adaptive goodness-of-fit tests are also built and easy to be employed: they are chi-square type tests. Simulations confirm the interesting properties of consistency and robustness of the adaptive estimators and tests.