Can someone help me? I have 2005 Ford Focus

Can someone help me? I have 2005 Ford Focus I have been having problems
starting it. No warning lights are on. Have taken it to Advance, Auto Zone, Ford,
AAA everything checks out. I can be driving down the road at times car jerk.
Sometimes when go to crank car will not crank I can try to tighten and shake
cables/wires connected to battery and go turn ignition it starts sometimes have
to repeat 2 to 4 times before start. I personally think rhe problem is conected to
the battery because the radio and clock come on after starts. Sometimes I have
to do that process everytime I get in car to go to work, back home, church etc.
Then sometimes do not have the problem for few days even weeks at a time.
Either way it go when start up car the clock/radio stalls to light up/come on. I
do not listen to radio no more so it comes on by itself when come it comes on
clock resets to 12 and radio come on automatically to am station with static
basically radio and clock reset self as if just put battery in