Can the interaction between a single long-term attractor and heterogeneous trading explain the exchange rate conundrum?

We study the US dollar, the British pound and the Japanese yen vs the euro over the period 2002-2016 using weekly data and we find that both types of agents react to the same transition variable, viz. the absolute distance of the actual exchange rate to its relative PPP value. The spot foreign currency demand of fundamentalists is driven by the size of the misalignment both directly and through a transition function, which models the adoption of fundamental strategies by newcomers. The number of chartists also varies according to the absolute distance of the exchange rate change from its fundamental PPP value. Evidence supports the existence of stabilizing and destabilizing behaviour not only by chartists but also by fundamentalists.