The setting is the North American Great Plains, mainly. Horses have already been introduced by the Spanish, but there is no mentioning of white man whatsoever in the series. (In one book, there's even a mention by an old tribesman that there's a mystery how the horse came to the land, and that it hasn't always been there.) It can therefore be assumed that Yakari's adventures take place after the 15th century, but long before the settling rush in the late 18th/19th century.