I have installed typescript for atom for writing Protractor Scripts For automation.
My code is written in Jasmine Framework as protractor supports it nicely.
Obviously, some of these issues (require and loginPage, for example) aren't necessarily anything to do with Jasmine. However, the issue is that these are global variables and the TS compiler can't find their declaration. The easiest way to remedy this is to declare each one at the top of the file in the following way:
declare var describe: any;
This will resolve the issues with describe and it. Other problems, such as require will be because you're not using the module import syntax.