Over the centuries people have associated the full moon with the paranormal and supernatural. And it would seem that the full moon phase can be a very favorable time to ghost hunt. The new moon phase is another time people associate with ghost hunting.
During a new moon, the moon rises at the same time as the sun. Because of the suns bright rays you can't see the moon, making it really dark for ghost hunting. But the best time to experiencing paranormal phenomena is two to three days before or after the full moon and new moon. Which would be a waxing crescent phase, the waxing gibbous phase, the waning gibbous phase, and the waning crescent phase.