Wavelet Theory And Its Applications To The Processing Of Economy And Finance Data

The wavelet 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 application 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. A study has been made of applications of wavelet theory to data processing of economy and finance data.It is a very important problem to reduce the redundancy of wavelet analysis in the study of wavelet theory. The second chapter discusses the classical theory in terms of the decreasing of the redundancy.A method is proposed for the analysis of the financial time series, which is based on the properties of multi-resolution and the thinking of denoise. A new model is given by analyzing the different decomposition parts of the time series. The model called time series decomposition and reconstruction model is based on wavelet analysis. Also, a new method of forecasting with wavelets is proposed. Corresponding to market fluctuate denoise, we pretend a simple denoise method based on the wavelet denoise.Wavelet transform has been applied to the study of financial market or stock analysis. It is a new try. The wavelet classical theory is used to discuss the behavior properties of share price signals. We show that there are the properties of self-similarity, periodical, and long-term trend in these signals. A study is made of the theory of linear fractal interpolation and a model called fractal interpolation approximate model is presented from the self-similarity of share price signals. Also, a comparison is made of the interpolation method and times. A detection approach based on wavelet transform is proposed for these self-similar signals, which is obtained from the properties of the self-similar process after wavelet transform.Some problems in the applications of wavelet theory are abstracted. Studying different problems by using different wavelet basis, we can obtain different results. Some properties of wavelets bases and their parameters are discussed. Also, discussions are made of the edges effect, the selection of wavelet functions and decomposition parameters, the singularity measured by Lipschitz exponents and the sampling of signals and wavelets bases.