So, [Wikipedia says] that the standard definition of independence is:

$f\_{X,Y}(x,y) = f\_X(x) f\_Y(y)$

How is this applied to timeseries? How do we calculate each side of the equation? 

If we're assuming that the probability distributions of the two series are the same, then $X=Y$ and we can just use $f(x,y) = f(x) f(y)$, right? So then I geuss I am basically asking what is f(x,y), and how do we calculate it?