EURUSD: BIG Picture with QE1+QE2+QE3 input. without ECB LTRO

Sometimes, we do forget to focus on the forest and therefore on on big picutre, because we are stuck focusing on one tree.
On the big picture, we see 3 inputs, which are QE1+QE2+QE3 and there effect on the market, the relaunch of it, the ending period and the effect on EURUSD.
With the end of QE3, baring in mind that FED President Yellen is still keeping the schedule of tappering, will there be a natural decrease of EUR against USD? Does ECB really need to decrease the interest rate to 0 or bellow in order to push EUR to loose value against USD? Or will it come naturally?
Bare in mind that so far ECB made a lot of statement, but no action. Perhaps ECB is waiting for the end of the EP elections, or ECB President will take a stance of FED. Let's wait and see.