Serial ranks have long been used as the basis for nonparametric tests of in
dependence in time series analysis. We shall study the underlying graph str
ucture of serial ranks. This will lead us to a basic martingale which will
allow us to construct a weighted approximation to a serial rank process. To
show the applicability of this approximation, we will use it to prove two
very general central limit theorems for Wald-Wolfowitz-type serial rank sta
tistics.