A Sequential Variance Ratio Test Based on the Closure Test Principle

Abstract: In a recent paper Chow and Denning (1993) proposed a multiple variance ratio test which controls the overall type I error probability when multiple variance ratio estimates are employed to test the random walk hypothesis against stationaryalternatives. In our paper we suggest the application of a sequential version which is uniformly more powerful but still controls the type I error probability for any set of true null hypotheses. Our test procedure is based on the so-called 'closuretest principle', which was introduced by Marcus, Peritz and Gabriel (1976). This principle constitutes one of the milestones in the theory of multiple comparison procedures and its application has resulted in the improvement of many classical test procedures.