A study of serial ranks via random graphs

Erich Haeusler, David M. Mason and Tatyan S. Turova

Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,

ISSN 0281-1944

Serial ranks have long been used as the basis for nonparametric tests of independence in time series analysis. We shall study the underlying graph structure 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 statistics.
Key words:
martingales, random graphs, rank statistics, serial ranks, wieghted approximations