That error message sounds like it might be a TypeScript typings problem, and the compiler doesn't know that there will be an Ajax object off of jasmine. It should be possible to generate some typings for jasmine-ajax and then hook them up to whatever existing typings you're using for Jasmine so the TypeScript compiler knows about everything.
Unfortunately, I haven't done too much TypeScript, so I'm not sure what all is necessary to make this all work.
Hope this helps. Thanks for using Jasmine!
-Gregg