As with booking flights from any website, there is no real answer to this question. There are lots of factors that go into airline ticket prices, so it’s hard to pinpoint when a fare will be at it’s lowest. However, Kayak does offer a few tools to help you.
The “Our Advice” box in the upper left corner of your search screen gives you a short-term prediction of how prices might change in the following week. You can also track your search by changing the Track Prices button to “On.” This will trigger a daily Price Alert email advising you of the current price trends for your search.