Predicting fares is like timing the stock market. Can't really be done on any kind of consistently successful basis.

Studies do show that, on average, the cheapest fares are usually offered about 60 days out. That does not always hold true though, particularly during high demand periods (e.g., Hawaii over Christmas). It's also likely to be less true with business class fares, because the cheapest discount business class fares often have lengthy (50, 60, or even 70 day) advance purchase requirements.

What you can do by following the fares for a while is know what's a good price so that you can pull the trigger when you see one.