Correlations between reconstructed EUR exchange rates versus CHF, DKK, GBP, JPY, and USD

On 1 January 1999, the European Union introduced a common currency Euro (EUR), to become the legal currency in all eleven countries which form the EUR. In order to test the EUR behavior and understand various features, the EUR exchange rate is artificially extrapolated back to 1993 by a linear superposition of the exchange rates of the 11 currencies composing EUR with respect to several currencies not belonging to the EUR, i.e., Swiss Franc (CHF), Danish Kroner (DKK), British Pound (GBP), Japanese Yen (JPY) and U.S. Dollar (USD) of interest for reasons given in the text. The distribution of fluctuations of the exchange rates is shown to be Gaussian for the central part of the distribution, and having fat tails for the large size fluctuations. Within the Detrended Fluctuation Analysis (DFA) statistical method, we have obtained the power law behavior describing the root-mean-square deviation of the exchange rate fluctuations as a function of time. For the period between January 1995 and January 1999, we have compared the time-dependent exponent of these exchange rate fluctuations for EUR and that of the 11 currencies which form the EUR. The German Mark (DEM) and the French Franc (FRF) have been the currencies primarily leading the fluctuations of the exchange rates, while Italian Lira (ITL) and Portuguese Escudo (PTE) are the less relevant currencies from this point of view. Technical considerations for the EUR implementation are given as conclusions. The cases of exchange rates with DKK appear quite different from the other four major currencies.