GH4 time lapse aperture issue

As aljudy mentioned, it's lens dependent, and can occur on any brand/mount. It's known as aperture flicker in time lapse crowds. Some lenses are more susceptible to this flicker than others. I think it's partially based on that having the aperture off by ~1/6 of a stop for still photos isn't that noticeable, so most lenses are built that way. (But as you see, very noticeable in time lapse)

Canon users even have the trick to "fix" the aperture by partially unmounting the lens while in preview mode, so the contacts aren't engaged. m43 doesn't have the trick, though.

Also most lenses show more flicker at the smaller (f11 to f22) end, as being slightly bigger/smaller (the aperture blades off) by a fraction of a mm at f22 is a larger percentage than off by the same mm would be at f4. As the blades aren't moved at a lens's wide open point, you don't get aperture flicker.

See if you can find other m43 time lapse people, and what they get from different lenses. My panny 14-42 rII is pretty good at controlling aperture flicker up to at least f8, but my 100-300 isn't as clean except wide open (but usable with PP, see next PP). I haven't used my other lenses in time lapse enough yet, as I usually leave my nikon D5100 to time lapse and my GX7 for taking-photos-while-waiting-for-the-time-lapse-to-end.

You also might want to look into PP software to manage the flicker. Even free apps like GoPro's have anti-flicker features. I use LRTimelapse ($$) or VirtualDub + an anti-flicker addon (free), but there are many other options.