Asymptotically pivotal statistic for surrogate testing with extended hypothesis

The method of surrogate data provides a framework for testing observed data against a hierarchy of alternative hypotheses. The aim of applying this method is to exclude the possibility that the data are consistent with simple linear explanations before seeking complex nonlinear causes. However, in recent time the method has attracted considerable criticism, largely as a result of ambiguity about the formation of the underlying null hypotheses, or about the power of the chosen statistic. In this communication we show that by employing a special family of ranks statistics these problems can be avoided and the method of surrogate data placed of a firm statistical foundation.