The Fractal Characteristics Of Euro Forex Market

This paper examines whether the fractal characteristics exist in Euro foreign exchange market or not based on the Fractal Market Theory(FMT) and utilizes plenty of statistical method for empirical study.The sample is to use the time series of exchange rate price of EUR/USD,EUR/JPY and EUR/GBP from 1^st Jan 1999 to 31^st Dec 2007.In the aspect of methods,this paper makes test of normality of daily return series of EUR/USD,EUR/JPY and EUR/GBP firstly,the empirical results imply that skewness of daily return series of three currency pairs is not equal to zero,and kurtosis exceeds 3 showing leptokurtosis.The estimated values of Jarque-Bera test statistics are much more than critical value of 1%and 5%level,which rejects the null hypothesis of normal distribution.Then the paper estimates daily return series of EUR/USD,EUR/JPY and EUR/GBP using classical R/S method,The results show that Hurst exponent of three currency pairs is equal to 0.60693, 0.62652 and 0.61521 respectively;the statistical cycle is 160 days,72 days and 68 days respectively;the correlative scale is close to 1.3196,1.3834 and 1.3464 respectively.After that, the paper makes comparative analysis between classical R/S and Lo's modified R/S,the result implies that there is 4.85%,1.17%and 5.25%bias in V statistic respectively and V statistic is greater than the value of V_n(q₀) in the short term under the effect of short relativity,and V statistic is close to the value of V_n(q₀) in the long term.Classical R/S probably overestimates long memory effect,and modified R/S leads to a result without notable long memory effect.At last,with GPH test,the paper estimates d,the long memory parameter, which is one characteristic of fractal theory,result shows that long memory exists in daily return series of EUR/USD,not in EUR/JPY and EUR/GBP.In the aspect of model building,the paper chooses mean model ARFIMA and variance model FIEGARCH reflecting long memory.According to Akaike,Schwarz,Shibata,Hannan-Quinn information criterium,order of the model is fixed and parameter is estimated. The empirical result implies return series and volatility series of daily exchange rate of EUR/USD show significant long memory and ARFIMA(1,d₁,0)-FIEGARCH(1,d₂,0) is the optimization model.Return series of daily exchange rate of EUR/JPY and EUR/GBP do not show significant long memory but volatility series show significant long memory,and ARMA(1,0)-FIEGARCH(1,d,0) is the optimization model.Leverage effect(including sign effect and magnitude effect) exists in volatility series of daily exchange rate of three currency pairs,positive and negative information takes persistent influence on volatility of Euro foreign exchange market and volatility intensity gets enlarged.The main conclusions from the empirical study as follow:there is distinct fractal structure in the Euro foreign exchange market,which is a typical fractal market.Euro foreign exchange market presents leptokurtic and fat tails and statistical cycle.Volatility series show long memory and leverage effect.