I use a generic set of rules to complement the airline revenue management systems (RM for short), because they determine the fare and that determines when you should buy the ticket.
The airline process of finding the right mix of fares for each flight is called yield, inventory or revenue management (RM). It is complex, using sophisticated computer software (and historical data in the software), that helps the airline estimate the demand for seats on a particular flight, so it can price the seats accordingly. And it is an ongoing process, requiring continual adjustments as market conditions change. Unexpected discounting in a particular market by a competitor, for instance, can leave an airline with too many unsold seats if they do not match the discounts. So the fares go up and down over time.
Up to 6 months before the flight, the RM systems are set on automatic and the fares are not especially cheap but they do adjust as sales fluctuate. Because no-one is actually watching them, the limits to the adjustment are deliberately quite constrained.
Then at 6 months, the RM people start to look at the individual flight once a week and adjust fares/ number of seats available to fit the sales pattern to their historical patterns. Now the fares can start to move. In a year when the travel world is generally a bit unsettled or there is a bit of a fare war on somewhere, then fares can suddenly change. At about 3 months in, the RM people start to look at the flight each day, and fare changes can come suddenly and unexpectedly. If sales in a class are up/down (maybe due to an unexpected concert at the destination or a cruise ship arrival where all the pax are linked to fares with another airline), then the RM people adjust the fares and numbers of seats.
When I have to buy air tickets, I start to look and have my money ready at 5 months out. It doesn’t always happen that a bargain leaps out then, but it does happen. We flew on a serious Middle East airline, first class, Oz-EU and back, for the business class price a couple of years ago. Otherwise I wait until the 2-3 months bracket and buy. So the short answer is that 8-12 weeks beforehand is where the best lot of good prices are likely to show. At 2 months out, it is probably too late to get a good fare. At one month, it is almost impossible. I despaired when one of my kids suddenly decided to join us on a trip Oz-EU but only a month before the trip. And this for a flight into the EU summer (which is prime air fare time). He flew the cheapest flight, which was Oz-Finland-Hungary in a marathon of obscure airlines and airports and hours – all for twice the normal price. And twice the elapsed time that we took. Seems to have improved his attention to air fare purchasing details though.