The mouse itself can produce keystrokes, it's a USB device. There may be a hardware issue / defect / failure in the mouse itself. Specifically if shaking the mouse stops it, I'd strongly suspect a defective mouse. Could be fixable by an electronics repair person (cold solder joint) Could also be due to low batteries, known to cause random malfunctions.
There's also a very remote possibility something is interfering with the wireless signal, another nearby device operating on the same frequency?
