Amethyst exposed to direct sunlight will *eventually* lose its purple color, but it takes a while -- several months in strong sunlight, many years for a piece of jewelry worn daily. As it fades, it will look lighter and lighter purple until, eventually, it's just grayish. But, as I said, that will take a while.
Here's a link to a decent article:
http://www.mindat.org/article.php/905/Amethyst+Specimens
The fading has to do with the instability of the iron impurities that cause the purple color.
Amethyst and citrine are both varieties of quartz with different mineral impurities. Most of the citrine for sale now is actually low-grade amethyst that has been treated.