This started happening to my 5S about a month ago. My screen would fade to what can be best described as an unsaturated shade of purple but within 20-30 seconds my screens colors would go back to normal. I thought my phone was in the first stage of a slow death. But the I noticed something strange. If I had my otter box (the kind that fully encases the phone and has a built in plastic screen cover) on my phone the fading NEVER happens. But whenever I take it out of the case it will start fading in and out for about 15 minutes. As long as I'm holding my phone and using it the fading doesn't reappear. It's a strange phenomenon and I can only guess that winters dry air is causing static electricity which in turn is interfering with my display. My otter box and my warm hands neutralize the charge and the fade stops.