An Analysis Of Exchange Rate Fluctuation Based On The GARCH Model With Wavelet Denoising

Reform of the RMB exchange rate system is a fundamental change for the RMB exchange rate mechanism,and such changes help maintain the RMB exchange rate at a more reasonable level.However,the RMB exchange rate determined by market also increases the exchange rate risks.In order to guard against exchange rate risks effectively,the inherent nature of the exchange rate volatility series must be found out.In order to objectively and correctly analyze that we can better grasp the regularity of exchange rate volatility series based on the use of the GARCH model with wavelet denoising,this paper first introduces the wavelet analysis theory.Wavelet analysis is a new branch of mathematics developing recently in applied mathematics,and it is regarded as one kind of mathematics tool that applys broadly.It already has been applied to sigal analysis,image processing,seismic prospecting and voice recognition successfully and has obtained exert-wide impact.Wavelets are a very interesting class of functions because of their special properties.The orthonormal bases can be constructed by translation and dilation of a mother wavelet.Wavelets have local property in time domain and frequency domain,so we can extract information from signals using wavelets.Wavelet analysis theory emerges as a new powerful mathematical tool in signal de-noise and data compression of process data analysis.In modern finance market,researchers found that most of the time-series,such as stock price,ratio,exchange rates and so on,the error series were non-autocorrelation,but the squared error series were autocorrelation,which indicate the variance or volatility were time-varying.Auto Regressive Conditional Heteroskedasticity model catches the charac- ters of this kind of economic variables.ARCH model is a kind of dynamic non-linear time series model.It reflects a special feature of economic variables-time-varying variances. However,financial data that we obtained often exists noise pollution,therefore this article attempts to use the method of wavelet thresholding denoising to carry out de-noising of the RMB against the U.S.dollar and the EURO exchange rate data series,compare different results using a different threshold functions and threshold calculation and select the best combination of de-noising.Then we use the EGARCH model to fit and predict data series after de-noising,and compare the results of prediction with that using the separately EGARCH model.The predicted results show that the prediction results based on the GARCH model with wavelet denoising are better than the prediction results based on the separately EGARCH model.So we can use the method to fit Perfectly the original data,reduce the error and improve error of Forecast.