Timesplitters is an amazing game series.
It was the best console fps and the most fun fps for me at the time they were released.
I played all 3 a lot on ps2, hundreds and hundreds of hours and I'm still playing those from time to time. I also made some speedrun/challenge world records in TS1 and TSFP.
As of today, sadly there will be no timesplitters 4, it's just impossible. Crytek bought Free Radical Design back then in 2009 and created Crytek UK with these people, but they never let them do a timesplitters game in 5 years, and last year there was a lot of problems with Crytek and Crytek UK, Deep Silver finally bought Crytek UK.
The thing is, Timesplitters series developers are now a part of Deep Silver, but the Timesplitters IP belongs to Crytek so if a Timesplitters 4 appears one day, it won't even have 1 developer that worked on the old games so it couldn't be as great...
However, a project named Timesplitters Rewind, a collection of the 3 first games is being created by some fans of the game, and they are allowed to use CryEngine 3. At first the game was for PC but it seems it will also have a PS4 version (and will maybe release on other consoles). I don't think the game will be released before 2016 though
Prediction: End of 2015 Hardware sales (as of January 20, 2015)
Wii U: 12.1M | XBO: 19.8M | PS4: 36.0M | 3DS: 58.5M | PSV: 11.7M