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Documents in EconStor mayThe wide fluctuations in the euro exchange rate since its launch in 1999 call for a deeper understanding of the underlying relationships. From a policy perspective, it is particularly useful to understand of whether and when exchange rate changes constitute movements towards or away from some long-term equilibrium level. While there are various ways to think about equilibrium exchange rates, this paper focuses on the universal starting point of applied exchange rate analysis which is to compare the current exchange rate against some measure of purchasing power parity (PPP). In its relative version, PPP states that nominal exchange rates move in proportion to relative developments in domestic and foreign prices implying a constant real exchange rate. While visual inspection seems to support that the euro real exchange rates oscillate around a mean in the long run, more rigorous statistical tests commonly fail to confirm such mean reverting properties.This finding should not lead us to the conclusion to discard drawing inferences from PPP analysis. Several caveats caution against a too strict interpretation of such tests of PPP. These include the lack of power of the tests themselves, the real exchange rate interaction with economic fundamentals (such as different trends in productivity) and the presence of nonlinearities in the mean reversion process. This paper investigates the latter aspect.Non-linearities in the adjustment of exchange rates can be justified from both a goods and a financial market perspective. As international goods arbitrage involves transaction costs, arbitrage sets in once the real exchange rate protractedly moves outside certain limits. From an asset market perspective, differing trading strategies could play a role with "Chartists" dominating market dynamics when the exchange rate is close to some perceived equilibrium, while "Fundamentalists" being at play once the exchange rate is increasingly misaligned.Appling this concept to the euro, the presence of such non-linear behaviour is confirmed for the real effective exchange rate of the euro and the two bilateral euro exchange rates with the biggest weight in the euro effective exchange rate, namely the real euro-dollar and the real euro-pound sterling exchange rates. Specifically, using a smooth transition autoregressive (STAR-) model, we find that the further away the real exchange rate moves from PPP, the stronger th...