A lot of pricing is magic, some is related to how business is going on this route & others, some is related to competition and some is supply & demand. Even if you could answer all those parameters, it would only be a guess what UAL might do.

There are some who try to do this, I can not vouch for their abilities
farecast
There is another but I can not recall who they are at the moment

or try e-mail alerts -- most all of the purchasing sites offer this

Another approach if you are sure you will be traveling -- buy now and track fares and re-fare if prices get better.