Wavelet Analysis And Its Application In Time Series

The wavelet analysis is one of most extensively discussed topics in the scientific and technical community. As an emerging mathematical branch, it embraces rich contents in it and with its potential widely applications. It has become a most effective tool for almost all subjects and engineering fields. It is significant in theory and practical in value to discuss the contents on wavelet theory in detail and explore its new applications.Recently, wavelet analysis has been introduced into statistics and caused a great change in statistical rearch. Traditional nonparametric estimation on certain assumptions about the smoothness of the function being estimated. With wavelets, such assumptions are relaxed considerably. Here , wo use wavelets to identify change points and estimate functions in time series.In this article, wo emphasize particularly on research of wavelet transform to singular signal, and analyse two kinds of singular points. We draw a conclusion that in the dectection of singular signal, wavelet function must be a 1 or 2 order of derivative of a lubricity function, and has regularity and compactly support set. The scale is appropriate. The estimateors of regression given by wavelets are consistent, and have been proved. Simulations show that wavelet method is effective.Detection of change points is a kind of im portent problems in statistic area. Commonly, to some extent, change point indicateabrupt-change of object, and has singularity. In this paper, we propose a mothed for the Detection of Change Points in Regressiong Model by wavelets. This mothed is different from traditional kernel estimate .The procedure is simple and intuitive.