We consider the statistical properties of the variance ratio statistic
in the context of testing for market efficiency defined by uncorrelated
returns. The statistic is then the ratio of the variance of
K-period returns to the variance of one-period returns scaled by
K. We use a continuous-time asymptotic framework whereby we let
the sample size increase to infinity keeping the span of the data fixed.
We also let the aggregation parameter K increase such that
K/T → κ as T, the sample size,
increases to infinity. We consider the limit of the statistic under the
null hypothesis and under three alternative hypotheses that have been
popular in the finance literature. Our analysis permits us to address size
and power issues with respect to κ and the sampling interval used. Our
theoretical and simulation results show that power is initially increasing
as κ increases but then decreases with further increases in κ.
This shows that for any given alternative there exists a value of
K relative to T that will maximize power. We thus
investigate the properties of a test that is the maximal value of the
variance ratio over a range of possible values for K. The
importance of the trimming to define this range is highlighted.This paper is drawn from chapter 2 of
Vodounou's Ph.D. dissertation at the Université de
Montréal (Vodounou, 1997). We thank two
referees for useful comments and Tomoyoshi Yabu and Xiaokang Zhu for
research assistance. Perron acknowledges financial support from the Social
Sciences and Humanities Research Council of Canada (SSHRC), the Natural
Sciences and Engineering Council of Canada (NSERC), the Fonds pour la
Formation de Chercheurs et l'Aide à la Recherche du
Québec (FCAR), and the National Science Foundation (grant
SES-0078492).