This dissertation makes systematic studies of the form of structures and nonlinear function approximation of the wavelet neural networks. It presents the universal approximation theorem and convergence theorem and the proof of theorems. It also makes detailed comparison among the properties of wavelet neural networks, BP networks and RBF networks.Based on wavelet analysis theory, various forms of wavelet neural networks are built. ①Based on continuous wavelet transform theory, the paper presents continuous parameter wavelet networks, whose activation function is continuous wavelet function. Furthermore, the parameters of networks are calculated by conjugate gradient algorithm or stochastic gradient algorithm; ②According to multiresolution analysis and orthonormal wavelet decomposition theory, orthonormal wavelet network is built, whose activation functions consist of orthonormal wavelet and orthonormal scaling functions. Hierarchical approximation algorithms are given. ③Orthonormal scaling wavelet network is proposed on the basis of the definition of multiresolution analysis. The BP algorithms for parameters of network are given. ④According to the basic principle of pattern identification of neural networks, a classified wavelet network for forecasting stock market is discussed. The dissertation made an investigation into the application of the wavelet networks to economic forecasting. Based on the wide-ranging application achievements of neural networks in the field of economic forecasting, we propose general methods and procedure for economic forecasting models based on various forms of wavelet networks, such as continuous parameter wavelet networks, orthogonal wavelet networks, orthogonal scaling function wavelet networks, classified wavelet networks. Through the research of various wavelet networks and their applications to the economic forecasting ,following nonlinear economic forecasting models have been established: ①establishing the nonlinear time series forecasting models based on continuous parameter wavelet networks, which are used in the simulated forecasting of the time series of generated the export and import values in China. ②applying orthonormal wavelet networks to the population forecasting of our country. ③establishing nonlinear forecasting models based on orthogormal scaling wavelet networks ,and then using it in the forecasting of the GDP of our country. ④according to the theory of "pattern reappearance" of stock technical analysis, we establish stock market forecasting models for forecasting "buying opportunity" based on classified wavelet networks. From the research and applied simulation of these wavelet networks, following conclusions can be drawn: ①the wavelet networks can effectively approximate in value the mutual relationship which is difficult to be quantitatively described by time series. ②the macroeconomic forecasting models based on wavelet networks can well described the nonlinear relationship in macroeconomic and make the established models much closer to the actual systems.③the wavelet networks not only posses the properties of self-adaptation, self-learning and strong fault-freedom of neural networks, but also make full use of the time-frequency localization properties of wavelet transform. The convergence rate of wavelet netwoks is faster than that of neural networks. Therefore, in the econometrics area and finance system, the wavelet networks bear especial functions and broad prospect for grasping and reappearing the time series character. |