fullcalendar & Angular 5
The issue you were having has now been fixed thanks to the GitHub issue you raised.
I believe running npm install --save-dev @types/jquery
will correctly fix this issue as i have encountered the same problem, and running this did the trick (after i found this post and the link to the GitHub issue).
to quote the fix on GitHub: "this is now accounted for in the docs: https://fullcalendar.io/docs/typescript/"