EURUSD is likely to continue its highly volatile lateral movement around is quarterly (66-day) moving average, within the approximate range of 1st standard deviations from the mean (their current span is 1.075-1.1340)
The price also is likely to hold within relevant highs and lows (that is to trade between 1.0450-1.1470).
Key reason for this is that EURUSD has become increasingly correlated to oil prices since the start of their decline back in the summer of 2014. Oil is very likely to move laterally for extended period of time from now on (see related idea), taking EURUSD with it on a sideways price action trip.
And the correlation is not accidental. The plunge in oil prices last year has initiated a broad advance in US dollar value against all key currencies (such as EUR, JPY and GBP), making it attractive to hold institutional funds in US dollars or dollar denominated assets.
Another factor supporting lower EUR (that is, holding it back from recovering its value) is the difference in monetary policies between USA and EMU. The Federal Reserve is increasingly talking about probability to raise interest rates within mid-term perspective, while ECB holds interest rates close and below zero and started its own quantitative easing program only last summer.
On the other hand, however, further significant decline in EUR (below the lows reached during recent months) also looks unlikely. Thing is, even stronger US dollar means even more pain to already suffering US exporters (their goods becoming less competitive on global markets in terms of prices) - a situation which US corporate lobby, Government and the Federal Reserve would really like to avert.