Did the Romans have any kind of a national day, or did the Romans have a name for the national day of some other nation? Such days go by various names in different countries (e.g. independence day or day of the republic), and I am wondering what the Romans might have called such a day. The exact definitions of a nation and a national day are not important; I am looking for attested names for celebrations of one's country (or similar) in ancient Latin literature. I don't really know how close ancient traditions come to modern national days, and that is part of what I want to figure out. This question was inspired by Finland celebrating its hundredth independence day today, on December 6, 2017.
The festival days for the birth of Rome was, at least in the late Republic, the Parilia.
Wikipedia has more:
By the end of the late Republic, the Parilia became associated with the birthday of Rome. Numerous accounts of the founding of Rome exist, but the particular one related to the Parilia is described by Ovid in the Fasti. According to this myth, Romulus, upon reaching Rome on the day of the Parilia, took a stick and engraved a line in the ground that defined the boundaries of the new city (pomerium). He then prayed to the gods Jupiter, Mars, and Vesta asking for protection of this area. However, his brother Remus, unaware of the boundaries, crossed the line and was struck down by Romulus's henchman Celer.
Over time, and under the influence of several Roman rulers, the structure of the Parilia changed. First, after Julius Caesar heard the news of Roman Victory at Munda in 45 BC (around the date of the Parilia), he added games to the ceremony. At these games, the citizens would wear crowns in Caesar’s honor. Caligula instituted into the celebration a procession of priests, noblemen, boys and girls of noble birth singing of his virtues while escorting the Golden Shield, previously bestowed upon him by the citizens of Rome, to the Capitol.