The Research On Nonlinear Dynamic Features And Component Prediction Of Exchange Rate Time Series

As an important variable in the international financial field, the exchange rate could determine the inner equilibrium and also influence the outer equilibrium of the national economy. With the development of the economic globalization and the acceleration of the international capital's movement, the exchange rate is becoming more and more important for the investor's making correct strategies, the enterprise's risk aversion, and the central bank's intervention in international exchange market. So, the behavior description and the forecasting's validity of the exchange rate variable has been becoming one of the most popular topics and focus in the financial research field.The traditional capital market theory has been established on the foundation of three hypotheses: Rational Investors, Efficient Market, and Random Walk. However, such equilibrium analysis system, which belongs to linearity methodology, couldn't provide reliable explanation of many odds lying in exchange market. Such as the"fat tails"in returns distribution and autocorrelation in time series, the volatility clustering, and the irrelevance problem between the exchange rate and the interrelated economic variables. The intrinsic characteristic of the capital market is not linearity, but nonlinearity. Therefore, the phenomenon that a new research trend comes to being could be taken for granted, which bases the point of nonlinearity and system evolution instead of in a linear and equilibrium view.This paper investigates the intrinsic nonlinear dynamics complex behaviors of five main exchange rates thoroughly, basing on the nonlinearity methodology and the hypothesis of heterogeneous expectations. The empirical sample consists of five daily exchange rates time series, including GBP/USD, CHF/USD, JPY/USD, SEK/USD and CAD/USD. The period covers more than 30 years, from Jan 1st 1975 to May 31st 2007. Finally, empirical researches have revealed that there really existing the nonlinear dependence, the long-memory property, the chaotic dynamic characters, and the multi fractal property.The BDS testing has been applied to detect whether the nonlinearity properties existing in exchange rates time series. Luckily, all of the empirical results refuse the null hypothesis (independent and identically distributed, iid). Besides the discovering of the nonlinearities dependence lying in the time series, the testing has been also put on the sub-sample series and the normalized series, to explore an intrinsic explanation for the existence of nonlinearity. At last, the results revealed that the nonliterary lying in the data may be caused by chaos.In order to detect the Long-Memory property, this paper applies the Rescaled Range Analysis(R/S), the Log Period-gram Estimation(GPH) and the Gaussian Semi parametric Estimation(GSP) on fifteen time series, including daily, weekly and monthly data of five exchange rate time series, by estimating the parameter d and Hurst exponents. The results tell us that there has do exist the Long-Memory property in all of the chosen exchange rates. It can be concluded that there is multi-scale self-similarity structure lying in the exchange rate time series. Therefore, the variable should follow Fractal Brown Movement, not the pure random walk (hypothesizes under the traditional capital market theory).In order to judge the existence of chaotic dynamical features in exchange rate time series, this paper applies the technique of phase space reconstruction and the algorithm of small data sets on the exchange rates. The empirical results show that all of the largest Lyapunov exponentsλ1 are above zero, and all fractal dimensions are no-integer, which suggest the existence of chaos. It not only helps us for knowing the behavior of exchange rates better, but also providing the possibility for short-term forecasting.Multi fractal theory is an important composition of fractal theory. After detecting the long-memory and fractal properties in the exchange rate time series, this paper puts the multi fractal analysis on exchange rates for more details. Firstly, the distribution diagrams of partition function have been applied for diagnosing the existence of multi fractal characteristic. After then, the multi fractal spectra have been used to describe the multi fractal characteristics. The discovery of nonlinear dynamic properties lying in exchange rate time series means that the volatility of the variables should origins from the nonlinear system itself, not only depending on the outer interrupting. Therefore, it's invalid for the national bank's forcibly intervention in the exchange market to make the price return equilibrium.Furthermore, after detecting the nonlinear dynamic properties lying in the exchange rate time series, this paper integrates the RBF Neural Network Model, the Lyapunov Exponent Predicting Model and the Volterra Adaptive Predicting Model into an Adjustable Component Predicting Model, in order to make a good predicting of the chaotic variable of exchange rate, and the weights of which could be adjusted by the time series themselves. The results of the empirical research on five exchange rate time series show that both the forecasting errors and the direction statistics of the Component Predicting Model could obtain better results than individual models, especially for the JPY/USD and the SEK/USD time series. Moreover, a compare of the predicting performance has been taken between the Adjustable Component Predicting Model and the Random Walk Model. Luckily, both of the D-M testing and H-M testing refuse the original hypnosis and the empirical results show that the Adjustable Component Predicting Model could obtain obvious advantages over the Random Walk Model as expected.