Aranuir's grandfather was Aranarth, the first of the Chieftains of the Dúnedain, who had seen the realm of Arthedain fall to the Witch-king, and the Witch-king himself then be driven out of the Northlands. Aranuir himself, son of Aranarth's heir Arahael, was born about a century after these events, shortly after the beginning of the time known as the Watchful Peace, and that peace continued throughout his life and rule. Aranuir succeeded to the Chieftainship when he was 93 years old, and due to the long life of his people ruled them until he reached the age of 163.
The date of Aranuir's birth appears only in The History of Middle-earth volume XII, The Peoples of Middle-earth. It cannot therefore be considered completely reliable.
2
The second element of Aranuir's name is possibly related to Sindarinnui, meaning 'ideas' or 'thoughts', suggesting that Aranuir was known for his intelligence, but this connection is speculative at best.