webdriverio: how to spy on a global object using jasmine

I'm trying to spy on the global google analytics method:

describe("google analytics spy", () => {
  let spy;

  beforeEach(() => {
    browser.url("http://...");
    let $window = browser.execute(() => window);
    spy = spyOn($window, "ga");
  });

 it("should invoke the ga function", () => {
   expect(spy).toHaveBeenCalled();
 });
});

Unfortunately, the returned window object is some sort of reference without any of its properties or methods:

{
  sessionId: 'somehash...",
  value: [],
  _status: 0
}

I can get a ga method by doing:

let $ga = browser.execute(() => window.ga);

which returns:

{ sessionId: '34dcfbd74e7eafac2eedc03ea1709858',
  value:
   { L: 1520951932160,
     N: {},
     P: [ [Object] ],
     answer: 42,
     create: {},
     da: {},
     getAll: {},
     getByName: {},
     h: { t0: [Object] },
     j: {},
     loaded: true,
     remove: {} },
  _status: 0 }

yet without any parent context, I am unable to spy on it. What am I missing?