[R] Sample correlation coefficient question NOT R question

[Leeds, Mark (IED)]

This is a statistics question not an R question. When calculating the
sample correlation coefficient cor(x_t,y_t) between say
two variables, x_t and y_t t=1,.....n ( one can assume that the
variables are in time but I don't think this really matters
for the question ), does someone know where I can find any piece of
literature that says that each (x_j,y_j) pair has
To be independent from the other (x_i,y_i) pairs  (j doesn't equal i )
in order for the calculation to have any reasonable meaning. This
makes perfect sense to me but I need it official writing so I can show
it to someone else because I don't know how to explain it. 
Obviously, there may be some way to calculate the correlation
coefficient when the (x_t,y_t) pairs aren't independent ( maybe ?) but
I am referring to the very standard correlation calculation ( pearson
for example or any other standard one  ).
Thanks for any suggestions/references/insights etc.
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