Ethiopians celebrate their New Year on September 16. I don't think that it is a coincidence it falls around the same date as the Jewish New Year, or Rosh Hashanah.
According to Ethiopian cultural accounts, the Ethiopian Queen of Sheba went to Israel to visit King Solomon to seek wisdom from the famous king.
Although this story is presented as a myth, I believe that the Queen of Sheba did exist. There is historical evidence, through written text, statues, carvings and burial sites, to indicate that such a queen did exist in the southern regions of what is now Yemen and northern Ethiopia, which would form the ancient kingdom of Ethiopia. At the time, Ethiopia was struggling with monotheism, and stories of a monotheistic country and king quite possibly reached the country and its queen, who then traveled to meet this legendary king.
Pre-Christian Ethiopians looked to Jerusalem when trying to understand their spiritual world, and as a way to get closer to this God. They were surrounded by pagan cultures, and isolated themselves, aided by the difficult mountainous terrain, to build their civilization based on this monotheistic premise. I believe the Queen of Sheba returned from Israel with many Jewish religious and spiritual insights, including the idea of this single God. She also brought with her the traditions of New Year as both a social and religious celebration.
In Christian Ethiopia, there is a special church service on New Year's day. The importance of the ram's horn in Rosh Hashanah, reflecting Abraham's sacrifice of the lamb, is observed in the social gathering of families. A ram is taken as a gift to the elder (often the grandfather) of the family, and slaughtered/sacrificed for the meal of the day.