How do I set a mock date in Jest?

I’m using moment.js to do most of my date logic in a helper file for my React components but I haven’t been able to figure out how to mock a date in Jest a la sinon.useFakeTimers().

The Jest docs only speak about timer functions like setTimeout, setInterval etc but don’t help with setting a date and then checking that my date functions do what they’re meant to do.

Here is some of my JS file:

var moment = require('moment');

var DateHelper = {
  
  DATE_FORMAT: 'MMMM D',
  API_DATE_FORMAT: 'YYYY-MM-DD',
  
  formatDate: function(date) {
    return date.format(this.DATE_FORMAT);
  },

  isDateToday: function(date) {
    return this.formatDate(date) === this.formatDate(moment());
  }
};


module.exports = DateHelper;

and here is what I’ve set up using Jest:

jest.dontMock('../../../dashboard/calendar/date-helper')
    .dontMock('moment');

describe('DateHelper', function() {
  var DateHelper = require('../../../dashboard/calendar/date-helper'),
      moment = require('moment'),
      DATE_FORMAT = 'MMMM D';

  describe('formatDate', function() {

    it('should return the date formatted as DATE_FORMAT', function() {
      var unformattedDate = moment('2014-05-12T00:00:00.000Z'),
          formattedDate = DateHelper.formatDate(unformattedDate);

      expect(formattedDate).toEqual('May 12');
    });

  });

  describe('isDateToday', function() {

    it('should return true if the passed in date is today', function() {
      var today = moment();

      expect(DateHelper.isDateToday(today)).toEqual(true);
    });
    
  });

});

Now these tests pass because I’m using moment and my functions use moment but it seems a bit unstable and I would like to set the date to a fixed time for the tests.

Any idea on how that could be accomplished?