Aggregation of the volatilities


I have seen in a previous post that the organizer would not provide the formula for the volatility computation.
But could you inform us about how we can aggregate the volatilities.
I guess, based on the baseline computed by taking the mean value of the volatilities of the day, that the volatility on a 1 hour time frame, is the mean of the 5 minute volatilites over 1 hour. Am i right?

This property does not have to hold.

One reason is that the baseline (“benchmark”) can be naive (no model is perfect, and the baseline can obviously be improved on): calculating the mean like in the benchmark doesn’t have to make full sense.

Another reason is that the property that you are guessing can only be approximate, at best: in fact, it makes sense that the volatility on infinitesimally small time slices be zero (prices do not have time to move), so the volatility on larger time slices cannot be calculated from the volatility on smaller slices (which are all zero, in this extreme case). So in general it doesn’t hold.

The baseline shows that it makes some sense to thus average volatilities (since predicting them this way gives a decent performance), but again doing this doesn’t have to (and cannot) make perfect sense.

Makes perfect sense, I just wanted to know if you used any kind of harmonization for the purpose of the challenge.
Thank you for your answer