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Using maximum of forecasted values to forecast maximum

I am using an algortihm to generate a daily sales forecast and have concluded that the forecast is, for pratical purposes, of good enough quality ("low" wMAPE).

In general, and without further information, is it possible to conclude something about using this Forecast to predict the maximum future sales over a time interval?

That is, if

$F1,...,Fn$

are presumed to be good enough to forecast actual sales values

$S1,...,Sn$

Can we state something about using

$max(F1,...,Fn)$

to forecast

$max(S1,...,Sn)$?