The spectrum of euro-dollar

Abstract

The purpose of this study is to analyse the time series of the eurodollar exchange rate. This exchange rate is studied as if it was a continuous-time physical process, which implies that we systematically make use of different degrees of time resolution. The analysis takes into account various statistical indicators, but puts a special emphasis on the spectrum of the process. In other words, we consider the process of the returns of the euro-dollar exchange rate as produced by a superposition of oscillations with different frequencies and we try to determine the relative weight of those frequencies within the returns process. The spectrum of this process is the function giving those relative weights. We find that this spectrum has an identifiable pattern and we claim that this pattern is a core characteristic of the process. We simulate then a process having the same spectrum and compare the behaviours of actual process and of the simulated process in terms of various statistical indicators. We find that the simulated process provides a good, but not perfect, replication of the behaviour of the actual euro-dollar exchange rate. © 2007 Springer Berlin Heidelberg.