Application Of Wavelet Network In Economic Prediction

Economic system is intrinsically nonlinear and nonstationary, making the gen-eral linear forecasting model is inaccurate. The neural network as an excellent tool for nonlinear function approximation, due to its nonlinear quality, self-organization, self-learning, robustness, distributed storage and parallel computing power, has been playing a more important role in economic projections. BP neural network is one of the most widely used neural network model, being proved that it has a strong spatial mapping ability. However, the result was not ideal when using BP neural network to do the forecasts. BP algorithm converges more slowly, and the network is easy to fall into local minimum when the parameters are selected inappropriately, which all affect the model's reliability and accuracy. Wavelet analysis with good time-frequency localization and zoom features, and with a strong nonlinear function approximation ability, becomes a strong black box identification tools in nonlinear system.In 1922 Zhang Qinghu and Albert Benveniste, from the famous French scientific research institutions, proposed wavelet neural network, composed of wavelet trans-form and based on neural network model, that is, using wavelet function to replace nonlinear activation function of neural network(such as the Sigmoid function). It integrates the wavelet transform and neural network organically and inherits the advantages of both. With the development of the nonlinear theory and artificial intelligence technology, wavelet network will be a strong tool in financial market analysis and forecasting.This paper attempts to analysis the structure and algorithm of wavelet net-work and propose four wavelet networks, two of which with the different network structures based on the same algorithm, namely Morlet-WNN model and Mor-let_Gaussin_WNN model; the others with the different algorithms based on the same structure, that is, the wavelet network based on the genetic algorithm and the wavelet network based on particle swarm optimization algorithm. Here uses wavelet networks for time series prediction,and makes analysis and comparison of the predicted results. The wavelet network based on the quantum particle swarm optimization is applied to forecast stock price in the last section. From the per-spective of quantum mechanics, Sun Jun and others proposed the quantum particle swarm optimization algorithm, which is a new PSO algorithm. They supposed that the particles have quantum behavior. while in the quantum space, according to uncertainty principle, the position and velocity of a particle can not be determined simultaneously, so that the particle can search for the global optimal solution in the whole feasible solution space. Simulation results is ideal.