Usually you want to test events so what you could do here is the following:
var spy = jasmine.createSpy();
this.component.on(document, 'myEvent', spy);
this.component.trigger('myEvent'/* , optionalData*/);
expect(spy).toHaveBeenCalled();
/* optionally
expect(spy.mostRecentCall.args[1]).toEqual(
optionalData);
*/
if in your component you trigger stuff after initialize, you may want to create the component, create the spy, listen for it, initialize the component at this point and then trigger and do the assertions.
You may want to sneak peek the other open sourced components or even the flightjs testsuite for more examples