what your talking about is time-lapse, its usually done by taking a number of photos at regular intervals say every 10seconds and putting them into software which plays it back at 20-30frames per second.
I've just bought an ion air pro (similar to the go pro but only £100 for the cheaper one rather than £200) to do the same type of videos with, i've just go to take it out and have a go shooting with it.
You can do time lapse videos with certain good cameras or some phone apps, although you'd have to leave it there for as long as you'd want the video to film for
Ashley