One of the biggest flaws in financial time-series analysis is looking at the data as a function of time.

Obviously it's the easiest way to analyze data, as we can plot it nicely, calculate the volatility, etc... but when we analyze data in a dimension of time we usually get https://twitter.com/Mephisto731/status/1344083746144841731

biased results. why? because we are extremely sensitive to our selection of sampling frequency/length of sample window.
Just think about the most useful tools in your quant toolbox : realized volatility and z-score...

Both are usually measured as function of time (and relative

to historical sample window), but who said that volatility evolves at t-fixed time intervals? the underlying fluctuation is not a function of time but the orderbook imbalance.
Also, let's say that I dynamically hedging my delta, am I really using fixed t-intervals, I guess not.

This gets even more interesting when we look at z-score, which is not only sensitive to frequency/window but the stdev of our window. when we sample an extremely quiet period we can observe 4-5stdev events that on a long-term average are probably 1-2stdev. does that make them

rare events? probably depends on the context...

And this is where I think most investors fall into the trap... not all volatility regimes were created equal.. if we analyze volatility time series we need to move from relative time window to a clustering/regime analysis

we can say that VIX at 20-30 is a sell (because Rvol is in the low 10s/high single digit)... but this is only if we look relative to historical window. If we look at it in the right context we might find that this is perfectly normal...

I remember that around mid 2014 FX vol hit 20-year low, and EURUSD vol was trying in the low 4s, I can assure you that those who bought it lost money (although implied traded at extremely low levels)... Once it moved to a new regime all of a sudden Rvol was starting to perform

and although implied was priced about 4-5vol higher Rvol was even higher.

My point, whenever you see extreme values, ask yourself if they are really extreme or it's our measurement that makes them extreme