Chaotic Empirical Research On The Exchange Rate Fluctuations Of RMB Against The U.S. Dollar

Exchange rate system is a complex giant system, there is a complex relationshipbetween the inside variables. The traditional exchange rate determination theorydeveloped based on linear models, can not reveal and explain the rule of exchangerate fluctuations. More and more economists, mathematicians try to use non-linearmethods and techniques to comprehensively summarize and refine nonlinearcharacteristics of exchange rate behavior, to explore operation mechanism ofexchange rate behavior under nonlinear paradigm, which have important theoreticalvalue and practical significance.This article applies chaos theory and methods to studying exchange data with thenormality test method such as QQ test, JB inspection, and conducting an empiricalresearch on its non-linear characteristics. The results show that the sequence ofexchange rate fluctuations do not follow a normal distribution; nonlinear structure testby means of BDS statistics shows that there is a nonlinear dependence characteristicsin the sequence of RMB against the U.S. dollar; characteristics of long-term memorytest via rescaled range analysis (R/S), Hurst exponent and V statistic shows exchangerate of RMB against the U.S. dollar has fractal structure. Analyze characteristics ofchaotic dynamics by means of phase space reconstruction, calculate the correlationdimension before the reform and after the reform which are respectively0.1416and1.0003, the largest Lyapunov exponent are-0.0010(<0) and0.0019(>0), thereforeobtain the criterion of the existence of deterministic chaos after the reform.Further analyze the chaotic results of RMB exchange rate fluctuations betweenthe “the reform" forward and "the reform" afterward, the study shows theheterogeneity of traders, the central bank intervention, path dependence ofinstitutional change lead to the chaotic differences.