Um estudo sobre wavestrap

Abstract

Wavelets are basis of function spaces that can be used to represent both continuous (functions) and discrete (sequences) signals; wavelets study gained great notoriety after the work of Daubechies, who developed a wavelet family with compact support (DAUBECHIES,1988). Also in the second half of twentiest century the great advances in computer processing allowed the emergence of various computation intensive methods, such as bootstrap (EFRON, 1979). One of the key assumptions to use bootstrap is that the sample elements are not correlated, generally that is not a characteristic found in time series analysis. This study presents a review on wavestrap: a technique that joins both wavelet analysis and bootstrap resampling. By applying bootstrap to the wavelet transform coeficients we can generate samples that retain roughly the same characteristics of the original signal. We also analyze other nonparametric con fidence intervals based on bootstrap for estimating the fi rst autocorrelation of fi rst order autorregressive processes.