The luminous fullness of the moon represents plenitude, abundance, and generous blessings. Therefore, the day of the full moon is considered a very auspicious time to initiate and to accomplish significant activities. The only full moon day considered an exception to this guideline is Holi Purnima (the full moon after Mahashivaratri) and the day following. These days are traditionally avoided for new beginnings.
The new moon is a time in the lunar month when the mind is especially quiet. It is therefore considered beneficial to dedicate additional time to meditation and chanting on this day as well as on the days before and after. Mahashivaratri is a Siddha Yoga holiday which falls on the new moon, and is traditionally a time for siddhayogis to chant the mantra.
The time of the new moon is not generally favorable for celebrations, significant activities, or new beginnings. The exception to this is the celebration of Indian New Year's Day, which occurs around the new moon.
For initiating significant activities, the bright half of the month, when the moon is waxing or increasing in light, is preferred to the dark half of the month, when the moon is waning. The increase of luminosity until the moon reaches fullness is traditionally equated with a strengthening of the forces that promote growth and prosperity.