hi david,

can square root rule be used in mean reverting condition?? rather than random walk??

and in autocorrelation condition, square root rule can not be applied to calculate multi-period var

am i right??

thanks David

Suk

Hi Suk,

No, strictly it cannot. The square root rule requires i.i.d. which is two requirements, mean reversion violates the ‘independent’ criteria. Basically, we use the square root rule in learning/basics, but owing to observed properties of returns/volatilties, in practice i.i.d. is violated and our square root rule is rendered inaccurate.

There is some ambiguity in the definition of “mean reversion,” which i tried to address in this post from August which you may find helpful (IMO, auto or serial correlations are more precise terms - some will use serial correlation to imply mean reversion)

“in autocorrelation condition, square root rule can not be applied to calculate multi-period var”
It can be done, the square root rule can be adjusted to handle the autocorrelation, but we do not study this in 2008 FRM. Our focus is the defect in i.i.d., specifically table 2.4 in Linda Allen which, to your point, says that mean reversion renders the square root rule to over or under state today’s volatility.

David