John Bergsma observes that the year of Jubilee was proclaimed with a trumpet blast on the day of atonement (The Jubilee from Leviticus to Qumran, 92), and draws this conclusion:

Since other ancient Near Eastern festivals of the seventh month—such as the akîtu—combined reassertion of the rule of the deity over his people (symbolized by enthronement), temple purgation, and (at least) symbolic acts of social justice,31 the proclamation of the year of jubilee on the Day of Purgation is fitting. A hard distinction between the religious ritual and social ethics is unknown in ancient Israel or the ancient Near East in general. As the people’s collective uncleanness is purged from the temple on the Day of Purgation, social and economic manifestations of the resulting cleanliness are also enacted.”

He notes that the double holiday also points to Yahweh’s reassertion of authority over His land: ANE kings proclaimed a release at the time of their accession, and so Yahweh proclaims a release “for the people of Israel at periodic re-affirmations of his kingship.”