In the recent Electronic Arts earnings call, CEO Andrew Wilson looked ahead to the next fiscal year (beginning April 1, 2016), saying we can expect a new Battlefield game this holiday, with a new Titanfall and Mass Effect: Andromeda releasing a bit later:

Looking ahead to FY2017, we will introduce breakthrough games from some of our biggest and most popular franchises. In Q1, we will begin with the creative and innovative Mirror’s Edge Catalyst from DICE launching in May. A great lineup of EA Sports titles are in development for next year and we look forward to sharing more about these new experiences in the months ahead.
An all new Battlefield game from DICE will arrive in time for the holidays. We are excited to have a new Titanfall experience coming from our friends at Respawn, and of course Mass Effect: Andromeda from the team at BioWare will launch later in the fiscal year. Players in our live services will continue to experience engaging new content, expansions, and updates and will have more new mobile titles as well.
Later on in the call, CFO Blake Jorgensen said the new Battlefield is likely to arrive in the third quarter of the fiscal year (October 2016 – December 2016), while Titanfall and Mass Effect: Andromeda should arrive in the back half of the year (October 2016 – March 2017).
As for the Star Wars game from Amy Hennig and Visceral, Jorgensen suggested it could be a few years away:

We are down to less than 15 major SKUs. And that feels...