The Study On The Non-linearity Of International Exchange Rate Based On Multifractal Theory

The foreign exchange market is an important part of the financial market.With the cross-border flow of commodity trade,services and international capital,the international financial market has become increasingly complex and volatile.How to grasp the complex characteristics of financial price fluctuations and reflect the evolution characteristics of the international financial market is very important.The traditional efficient market theory and linear research paradigm are challenged and questioned,while the development of non-linear scientific theory provides a new direction and thinking method for the research of financial market.Fractal economics is one of them.As a cutting-edge tool of complexity research,fractal theory and method can depict the complex volatility of financial market.Therefore,based on the nonlinear theory,this paper studies the non-linear dependence,multifractal characteristics and the source of multifractal and then predicts of the exchange rate price trend.The specific work is as follows:(1)The J-B test and Q-Q normal test are used to verify that the exchange rate of return series do not obey the normal distribution,and the non-linear dependence test is based on BDS statistics.All the test results of the exchange rate return series reject the original hypothesis of independent and identical distribution,and further test the correlation of the data.The test results show that there is a low linear correlation in the exchange rate return series,so the non-linear dependence becomes the main reason for rejecting the independent and identical distribution.(2)The general Hurst index and multifractal spectrum of exchange rate return series are measured by MF-DFA method.This paper demonstrates the existence of multifractal phenomenon of exchange rate of return series.The classic Hurst index H(2)> 0.5 of all exchange rate of return series shows that exchange rate data has long memory,among which RMB and New Zealand dollar have the strongest long memory.The widest multifractal spectrum of sterling indicates that the market volatility of sterling series is the largest and the risk is the largest.(3)The source of multifractal characteristics of exchange rate are analyzed.By means of random rearrangement,phase reconstruction and iterative phase reconstruction,the main factors that may cause multifractal characteristics are tested: the correlation of the fluctuation,the fat tail distribution and the nonlinear correlation of the fluctuation.The MF-DFA method is used to calculate the generalized Hurst index of rearrangement sequences and substitution sequences to obtain the empirical distribution,and propose three hypothesis testing methods.These methods can explain the cause of multifractal more than the single rearrangement or substitution sequence analysis method,and can show more detailed information of the cause of multifractal formation.The empirical results of three hypothesis tests show that the cause of the multifractal characteristics of the exchange rate return series is the nonlinear correlation and fat tail distribution of the volatility,and the nonlinear correlation is the main reason.(4)The price trend of exchange rate is predicted.Based on the long memory feature of exchange rate series,ARFIMA model is used to model and predict the long memory series.RBF neural network and volaterra series adaptive model are constructed based on the nonlinear feature of exchange rate series.According to the principle of error minimization,a combined for ecasting model is constructed.Through the analysis of error performance index,the combined forecasting model has obvious advantages over the individ ual model.