If history is any guide, that is.
The website Quartz recently did a study of data from booking engine Kayak.com and determined that the cheapest holiday airfares, last year, were sold in early October. In fact, for both Christmas and New Year's, the lowest airfares, for travel within the USA, were purchased on October 11. So set an alert folks!
Alas, the window for Thanksgiving airfares has already passed (again, if we can trust last year's stats). The lowest priced tickets then (again within the US only) were sold in September.
For all three holidays, airfares commenced a steady march upwards after these dates had passed, getting to their highest levels right before the holidays. So don't wait around, assuming you'll find a last-minute deal. Now's the time to book!
As for international fares, the pictures a bit muddier, but with them, too, the priciest fares were sold in the month before the holidays.