Research On The Volatility Of USD/RMB Exchange Rate Based On Fractal Theory

With the process of global economic integration,trade between countries is increasing and the exchange rate also gradually became the bridge of various countries' economy.Exchange rate fluctuations will not only impact to the growth of the national economy,but also can give the micro economy huge risk.To guard against foreign exchange risks which result from exchange rate volatility,characterization and prediction of exchange rate volatility is particularly urgent and important.In this paper,on the basis of reading a lot of literature,we first overview the basic content of the efficient market theory,and through using a series of methods to do empirical research on the USD/RMB exchange rate such as the JB test,Q statistic,ADF test,the ARCH effect test,etc.The USD/RMB exchange rate shows the characters of non-normality,auto-correlation,non-stationary,wave agglomeration,volatility clustering and long memory,and it doesn't conform to the characteristics of the financial markets under the efficient market theory.Second,introducing fractal theory,we use box counting method and q interval structure partition function method to test the fractal characteristic of USD/RMB exchange rate,and then do the multifractal spectrum analysis.The study shows that USD/RMB exchange rate has multifractal characteristic,and the correlation of the standard deviation of scaling exponent and USD/RMB exchange rate volatility is extremely strong.Again,through multifractal spectrum analysis results we establish multifractal volatility measures and USD/RMB exchange rate volatility dynamic model which is based on fractal theory.We also carry on the empirical research and test the validity of the model.Finally,by applying the method of rolling time window,we select GARCH model as reference model and analyze the effectiveness of the proposed model on the exchange rate volatility forecasting.We put forward the corresponding policy recommendations in order to maintain the value of RMB stable and promote the healthy development of China's foreign exchange market.