How do you know if Turkish Airlines will raise or drop the prices?

A week ago i checked for prices from Boston to Venice and it was over $1400 and a few days later it dropped to $1115. The tickets are for June 29(ish, whenever it's cheaper) till July 15th.
How do I know if the prices will raise or drop? Should I buy it while it's cheaper or wait and risk it, hoping they will go lower…

They let you know if you have an account with them.

There's no guaranteed way to decide which flights might increase or decrease in price, tomorrow, next, week, or next month.
As there has been a huge drop in the number of plane seats available this summer for travel around the planet. Expect prices to increase at the start of the PEAK HIGH DEMAND travel time.

I found a fare of $1095 for your dates and one of $1015 departing June 27 in a few seconds.

I doubt you are spending your entire time just in Venice. Suggest you also explore a return flight from some other place.

Travel Agents spend their entire day searching for the deals and cheaper routes. It is how they make a living.

You are welcome to spend hours of your time to save a dollar or two or hundred. Or just let a human get a commission instead of the computer booking site that just searches for the FASTEST way.

Gosh just checked another site many use. A fare of $909 for your dates on United.
Just under $900 if you go Sun June 30 and return Fri 12 , or Tues 16 Wed 17 Thur 18. Your Monday return is the expensive day.
this site is advertised on television often.

Good luck in your search. Not bad. Only you can place a value on your search time to save another hundred. Or two.

There are probably more cheaper ways that just take a little longer. Is it so horrible to spend a day or some extra hours at some change of plane place going there or returning.

A day in Rome and few hours train ride to Venice. A day in Frankfurt or some other place.
Keep searching if you want the bargain, discount cheapest fare possible.

As a general rule airline fares are determined by Supply and Demand. The more demand their is for a flight the higher the cost will be.

The prices were lowered for these flights because they are not being booked at the level the airline wants. Now, once the airline gets to the level of booking they are looking for you can expect the fares to increase again. Especially as the flight date gets closer.

So you can gamble that the prices will go lower, but you could also find the prices jump back up again overnight. The advantage to waiting if you are willing to accept a higher price is you may get a lower price. The disadvantage is that you may end up paying the higher price.

If you take the time you can continue to monitor the prices for further drops, but if you notice the trend up it would probably be time to purchase the tickets. Also, when you purchase the tickets be sure to purchase them directly from the airline.