Compactly Supported Orthonormal Wavelet And Wavelet Theory In Economic Forecasting

Wavelet analysis has been the focus of attention of many subjects since 1980s. And its applications have been involved in almost all branches of engineering and natural science. Now, wavelet analysis has become a powerful tool for solving many complex problems in natural science and engineering. In this paper we explore and study the algebraic method for construction of compactly supported orthogonal wavelets and application of the wavelet analysis theory to economic forecasting.1. Construction of compactly supported orthogonal wavelets. As the importance of compactly supported wavelets, many people committed to this problem, and obtained a lot of useful conclusions. On this basis, we study the algebraic method for construction of compactly supported orthogonal wavelets to draw some conclusions, and apply this method to find some examples of wavelets.2. Application of wavelet analysis theory to economic forecasting. Since wavelet analysis is a powerful tool for signal processing, and a number of economic data can be seen as a signal, so we can use wavelet transform to deal with economic signals to expect better results. We take an example here and compare with the least squares to try to explain the superiority of this method. In the end, the wavelet networks, which combining wavelet with neural network, is also introduced with application to economic forecasting.