The current understanding is there is no left limit.
In practice, it it limited by the observation time, however the main puzzling feature of 1/f noise is the absense of the 1/f limit.
That also creates main obstacle to build universal thery of 1/f noise: the correponding devices e.g. small transistors simply do not have media to store information to support noise self-correlation seemingly going infinitelly into the past (unlike classical random walk it can be shown that self-correlation of 1/f noise cannnot be 'stored' in one-two 'variables').
One can see some review on the topic https://arxiv.org/pdf/physics/0204033
I personally work on some approach explaining 1/f noise as 'quantum walk' inside some graph defined on Gilbert space of wavefunctions, that graph having non-trivial two-metrics topology ( a bit like Faceebok : there is geographical distance and 'number of shandshakes' distance). That approach allows to treat 1/f noise as intermideate case between classical 'random walk' (having 1/f^2 noise spectra) and white noise (having flat noise spectra). However, that approach effectivly removes the concept of 'wavefunction collapse' thus propelling 'multiverse theory' to be more that just 'interpretation'. Or, to say poetically: 1/f noise is the 'hustle' of diverging 'multiverses'.
Treating 1/f noise as essentially quantum was nailed in the 1970s by Peter Handel, however he was (wrongly) treating it on the level of wavefunction of individual particles, not system and got (mostly unjistified) extremelly harsh treatment by scientific community of time, that is despite getting some insight into experimental outcomes.