No reason at all for the optimal window size to be the same. Example:
A_i(t) = M_i(t) + E_i(t), i = 1,2
M_i(t) is reset to a random value every S_i days,
E_i(t) is white noise, independent of everything else.
Now, imagine that
S_1 = 10,
S_2 = 20.