Yup, it has the fun property that you'll get the same error in your estimate of the mean regardless of averaging time (though since it's not stationary this isn't even really that well defined).

The paper linked at the "see also" section ? (thx)

As noise, its 1/f is 0.748544393 years per comment, haha.

(The frequency is 42.3338481 nanohertz.)

It's not completely unexplained. Roughly speaking you can get that power spectrum in the limit when you are adding up many different events where the magnitude of the event is inversely proportional to its likelihood (and in practice, there is a limit to the magnitude of the events that will cause it to level off at some point, but for some processes this is not measurable even over decades). The main mystery in most cases is what exactly is the physical process that is causing it. For some electronics it looks like it is due to trapped charges sometimes tunneling around, but it doesn't explain every case of it in electronics let alone everything else. Convective thermal effects can also be a good candidate in a lot of systems, since turbulence also has 1/f noise properties.

(Also, the low frequency range on a DFT can look weird for reasons other than noise: it'll also tend to rise up if there's any longer-term structure to the signal as well, so you need to be careful interpreting them blindly if you're trying to measure noise)

Low frequencies are studied quite extensively, especially the mHz-10Hz region for noise characterization of solid state materials. 1/f is quite well studied depending on your field. In semiconductor physics, for example, one possible explanation is electrons trapped in defects or on charged islands and then slowly trickling down. Of course this explanation cannot be used in other fields where 1/f noise shows up as well. The problem is that no model gives a satisfying answer as to why it occurs therefore its unexplained. Lack of model doesn't mean that you can't engineer your way around 1/f noise for example the chopper amp works so well because it shifts away towards frequencies above the 1/f cutoff.

Pink noise is also perceptually flat noise, because it contains the same energy in each octave (or decade). 'truly' white noise (equal energy for equal bandwidth) tends to sound quite tinny/hissy in comparison.