Weren't the Romans Caucasians? I don't know, just asking.
Partly... Let's say that in 200 BC, they were a mix of Romans (Greek colonists), Egyptians, and some Caucasians. Their traditional tale about the establishment of Rome (Romus, Romulus and the she-wolf) makes them descendants of the Trojans (who were of the same kind as the post Mycenaean Greeks) . Caucasians were: -goths (Ostrogoths, Visigoths), the Norse tribes (giving rice to the Normans) the Franks, the Slavs, the Arabs and the East Indians. (But with a lot of intermixing with the original populations.)
There was a documented movement of people from and around the Caucasus mountain area westward and southward, that started at about 1150 BC and probably triggered by a decrease in local resources and an increase in coagulation of tribes eastward of them (see: Moguls) that had territorial ambitions. So it was “Go west (and south) young man (and lady)” for these folk back then.
The term “Caucasian” to describe white people was an inception of Johann Friedrich Blumenbach, an anthropometrist who based on cranial size, used it to describe people of “Aryan” (i.e. white European), “Semite” (i.e. Jewish) and “Hemite” (i.e. Arab) origin. Unfortunately, the term, got coined in a matter that it unfortunately describes any person with light skin these days…