I've been working in and following the travel industry for decades. Unfortunately (for consumers), FCDub's statement about not knowing if prices will go up or down is pretty true.
The only real exceptions to that statement involve times of extreme demand. Examples: Some dates are Thanksgiving, Christmas, and Spring Break for Florida.
At other times, the only way to know pricing strategies is if you have access to proprietary information at each airline. And even then you might not know because the majority of decisions are made by software using insanely complex math.
My Advice: Check the prices for days around when you are traveling (even if your dates are set in concrete). Also, check the same day of week plus/minus two weeks (i.e. if you're flying on a Friday, check the two previous and subsequent Fridays). Doing all of that might give you a glimpse into whether your travel days are special. If your days are substantially higher than other times, that's an indication that there might be a special event (like a major convention) that is driving up prices. In that situation, prices are unlikely to drop. If pricing is similar all month, there's a far greater chance of price fluctuations.