Research On Combined Forecast Of Exchange Rate Based On Neural Network And Fractal Interpolation Of Chaos

Effective prediction of exchange rates will not only affect the economic and trades of countries,but also prevent the happening of the international financial crisis or reduce the damage.The traditional research methods and models cannot fully explain the complex nonlinear system of foreign exchange fluctuation.However,chaos plays an important role in the study of nonlinear.We try to use chaos theory to study foreign exchange fluctuation,explain and predict the complex nonlinear system.First,we did an empirical research of nonlinear characteristics on the exchange rates by using graphic method and index method.Next we got the time delay,embedding dimension of three exchange rate time series by using C-C algorithm and then got the maximum Lyapunov index and fractal dimension by the Wolf algorithm and G-P algorithm on the basic of reconstructing the phase space to verify the chaos of exchange rates.After this we set up the prediction models based on the chaotic characteristic of exchange rate.We set the best embedding dimension of reconstruct phase space of chaotic system as the number of input layer neurons and temporal vectors as the input neurons when constructed neural network.By the fractal dimension we can get the vertical scaling factor and set up the fractal interpolation model.Finally,on the basis of predicting by two models we made an empirical study of dynamic combination forecasting according to the principle of a small proportion for larger error in the combination forecasting model.According to the statistical description we can get that the exchange rates do not obey the normal distribution and have nonlinear characteristics.The three largest Lyapunov index is positive and the fractal dimension is smaller fraction.It is proved that three exchange rate time series are low dimensional chaotic system with sensitivity to initial conditions.By the combined forecast model of exchange rate based on the chaos theory we can make an effective use of the ability of explaining complex systems of chaos,at the same time we also can combine nonlinear approximation ability of neural network with not smooth curve fitting ability of fractal interpolation.The results show that the combination forecast model can keep the advantage of two prediction models at the same time reduce the defects in the single model in the prediction,effectively improve prediction accuracy.