I'll add my approach to the answers, so it doesn't get lost in the comments:
Short answer: No, there is no single event for user activity.
Long answer:
I think the approach here is to define a number of events which are considered "user activity" like mousemove, keyup or focus/blur on formfields and then set up a listener to these events. This can be easily done in jQuery like already explained here:
jQuery multiple events to trigger the same function
Depending on the actual page (which we dont know anything about), there could be more events besides mousemove, keyups, focus/blur on all formfields that are considered user-activity. Closing a popup for example.
To listen to more events, check https://api.jquery.com/category/events/
Hope this helps.