Check the ECU wires and the battery on the car - It could be a short or loose wire and the car is actually is shutting off but it starts itself up again because the car is moving - (its basically push starting itself) this happend to a friend of mine his car was jerking around when driving sometimes and we figued out one of the battery terminals was grounding itself out on the rear wall of the engine bay sutting the motor of for a brief moment.

Hope this helps.