False EUR Exchange Rates vs. DKK, CHF, JPY and USD

Abstract

The Euro (EUR) has been a currency introduced by the European Community on Jan. 01, 1999. This implies eleven countries of the European Union which have been found to meet the five requirements of the Maastricht convergence criteria. In order to test EUR behavior and understand various features, we have extrapolated the EUR backwards and therefore have obtained a false euro (FEUR) dating back to 1993. We have derived the exchange rates of the FEUR with respect to several currencies of interest not belonging to the EUR, i.e., Danish Kroner (DKK), Swiss Franc (CHF), Japanese Yen (JPY) and U.S. Dollar (USD). We have first observed the distribution of fluctuations of the exchange rates. Within the Detrended Fluctuation Analysis (DFA) statistical method, we have calculated the power law behavior describing the root-mean-square deviation of these exchange rate fluctuations as a function of time, displaying in particular the JPY exchange rate case. In order to estimate the role of each currency making the EUR and therefore in view of identifying whether some of them mostly influences its behavior, we have compared the time-dependent exponent of the exchange rate fluctuations for EUR with that for the currencies that form the EUR. We have found that the German Mark (DEM) has been leading the fluctuations of EUR/JPY exchange rates, and Portuguese Escudo (PTE) is the farthest away currency from this point of view.