This Great Graphic, created on Bloomberg, is a long term chart of the euro. Each bar represents a month and the purple line is a 120 month (ten-year) moving average. It comes in now just below $1.32.
Purchasing power parity is understood by economists as the level currencies gravitate around in the long-run. A long-run moving average is by definition a level the currencies gravitate around in the long run.
The long-term moving average may offer a quick guesstimate of PPP or fair value. The OECD's measure of the euro's PPP is near $1.24. At current prices the euro would be about a dime or around 7% more than OECD's fair value estimate. Among the major currencies a 7% deviation from fair value is well within the normal vagaries.