The most likely problem is something stuck or shorted in the wall switch or the wiring for the wall switch that is intermittently sending a signal to open the door.
If the wall switch checks out okay then you might have remote with a sticking button or low battery or failing altogether and that is putting out the signal. If the batteries are all good, you can try resetting the memory on your opener and reprogramming your remotes to help hopefully resolve the issue or help pin-point a bad remote. There are programming instructions in your manual and also in the links below.
If everything else checks out, there may be interference in your area in a similar range to yours, that might be a neighbor who somehow ended up with a similar program remote to yours or an old remote somewhere in a drawer with a button pushed, or even a new satellite dish or appliance or phone lines. If nothing obvious is found you may want to consider consulting a professional who can look for signals with a meter.
And finally, it could be something shorting on the logic board of the opener itself. In that case you would need to replace the board. Again, you may want to consider consulting a professional at that stage considering the cost of a replacement board.