UIP obviously stands for Uncovered Interest Parity. The following is a crude visualization of its explanatory strength. The graph depicts the difference between real 12-month Libor rates for Euro and USD against the change in the US/Euro exchange rate. An increase in the real spread should lead to a Euro appreciation with the two graphs moving in the same direction (data are monthly since January 2007):
It is quite evident that the two series are highly correlated (correlation coefficient of 0.65 with R² equal to 0.42). What is very interesting is the fact that the spread is driven by inflation differentials between the Eurozone and the US (as a result of current disinflationary forces in the Euro area), since nominal rates have converged in the two regions:
Obviously the above graphs are rather crude and a better indicator of future inflation rates would be inflation swap rates. These might help explain recent exchange rate movements (which are not easy to explain in the first graph).
In any case, the relative unwillingness of the ECB to act upon the disinflationary forces in the Eurozone does have its toll on the exchange rate which might negate a large part of the improvement of the RER. How far inflation rates will remain weak is going to play a crucial role on future exchange rate movements.