I would try turning up the bounces (especially glossy) 3- 4 is a bit low try 9-12 and render a few frames to see if it helps, it looks like the reflection rays of the lights sometimes hit and sometimes miss.
Also I seem to remember that light tree can give different results per frame (I could be wrong on this but it is worth a try to turn it off if you have it on)
I’ve found the solution to be to raise the threshold to about 0.03 (this works for this particular scene) and the samples to 10000. By increasing the samples to this high number, it provides sufficient information to eliminate the shimmering.
Turning up the bounces or turning off the light tree doesn’t seems to make a difference.
Yes, you have actually two ways to do this, either to increase your samples up to something very high, or to use 3rd party apps in order to remove that noisiness