Dynamical Analyses of the Time Series for Three Foreign Exchange Rates

Abstract

In this study, we investigate the multifractal properties of three foreign exchange rates (USD-KRW, USD-JPY, and EUR-USD) that are quoted with different economic scales. We estimate and analyze both the generalized Hurst exponent and the autocorrelation function in three foreign exchange rates. The USD-KRW is shown to have the strongest of the Hurst exponents when compared with the other two foreign exchange rates. In particular, the autocorrelation function of the USD-KRW has the largest memory behavior among three foreign exchange rates. It also exhibits a long-memory property in the first quarter, more than those in the other quarters.