Does it turn off by itself or only on?

Televisions, unless unplugged, always have electricity running to the power supply. An on/off problem would most likely be in a component there.

Could there be any other device near the TV that could be triggering the set to come on? DVD Player? VCR? Cable box? Most of these have the ability to control multiple units. Remove them from the area to see if they are the cause as well. They may need new batteries.

If you turn the TV off, will it come right back on immediately?

Does it make any noise when it turns on by itself?

Is there a consistent timing factor involved? For instance, if it turns off by itself, does it do this if the TV is on for 3 minutes?

Once when I first got Dish my neighbor was turning mine off somehow. Their customer service figured it out somehow.

I've an old $79 TV that gets on one of these trips quite often. Just unplugging it for 15 minutes may fix it for a day or a year.