Albert Barnes Commentary 1 Kings 12:32

"And Jeroboam ordained a feast in the eighth month, on the fifteenth day of the month, like unto the feast that is in Judah, and he went up unto the altar; so did he in Beth-el, sacrificing unto the calves that he had made: and he placed in Beth-el the priests of the high places that he had made." — 1 Kings 12:32 (ASV)

A feast - This feast was intended as a substitute for the Feast of Tabernacles. It may also have taken on the character of a dedication feast, held at the same time, following Solomon's example (1 Kings 8:2). His reason for changing the month from the seventh to the eighth, while keeping the same day of the month, is not clear. Perhaps it was because of the later vintage in the more northern regions.

It is noteworthy that Josephus places the scene in the "seventh" month. Therefore, he was apparently unaware that the people of Israel kept the Feast of Tabernacles a month later than their brethren in Judah. The expression "he offered upon the altar" shows that Jeroboam himself officiated as a priest and offered this sacrifice at Bethel, not at Dan. At Dan, it is possible that the priests descended from Jonathan—the son of Gershom and grandson of Moses—were the ones who undertook the services (Judges 18:30).