Tests and Properties of Variance Ratios in Microstructure Studies

The properties of variance ratio tests across trading and non-trading periods are examined using the generalized method of moments. For the case of opening and closing return variances, the joint tests indicate that the null hypothesis that the variance of opening returns equals the variance of closing returns cannot be rejected for a sample of New York Stock Exchange stocks. This example demonstrates the importance of accounting for overlapping observations and cross correlation in such frameworks. The conventional average (across assets) variance ratio test is shown to be biased against the null in small samples. Specifically, when non-zero correlations are ignored, previous tests have the wrong asymptotic size. This bias persists in other frameworks as well: although this study confirms earlier findings that the return variance during non-trading periods is significantly lower than during trading periods, test statistics that ignore correlations are shown to be inflated.