The cursor shouldn't move on its own unless there is a hardware issue, or you have a virus, malware, etc.
Try starting up the laptop in "Safe Mode" and see if it acts normal in there. If the cursor acts fine in there, then it is something on the device. If it still does it in there, then it is probably hardware.
How to enter "Safe Mode" when booting the computer.
In Windows 8 and 10...
As your computer restarts, press F8 (possibly a few times) to enter "Safe Mode"
a. Press the "F4" key to Enable "Safe Mode".
(The computer will then start in "Safe Mode" with a minimal set of drivers and services.)
b. Press the "F5" key to Enable "Safe Mode" with Networking.
( Once "Safe Mode" with Networking starts, Windows is in Safe Mode, with...