Application des ondelettes à l'analyse des séries chronologiques.

Abstract

This theme is the study of wavelets and their applications to the statistical analysis of stationary time series and non-stationary. Wavelets provide an interesting mathematical tool to address some deficiencies encountered in the conventional Fourier analysis. After a brief review on Fourier transforms, wavelets are introduced and their evolution over the last 03 decades. It addresses the essential theme of this work involves the application of wavelet time series and especially to the class of long memory process. This work includes the following: 1-The Fourier transform and its applications in time series.2-Introduction to Wavelets: history and correct application of Fourier transformation. 3-Applications of wavelet stationary ARMA processes and long memory process with a fractional Brownian motion model. 4-Simulation of the three samples of an AR (1) and the comparison of the classical periodogram wavelet periodogram after the Gaussian wavelet.