A study of serial ranks via random graphs

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.