Funny feature of serial correlation coefficient...

Hallo,
let {x_0,x_1,x_2,...} a sequence of outcomes of the random variable X
which can take only two values 0 or 1 (the sequence can be considered
as a string of bit). Does anybody knows where I can find the proof
(books, weblinks, papers...) that the serial correlation coefficient
(SCC) with lag 1, corresponds to the sum of transition probabilities
between an outcome and the following one:

SCC(x_i,x_(i+1)) = p(1->1) + p(0->0) - p(0->1) - p(1->0)

Thanks for any reference!

David Tischler

.

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