Tbe Review of Financial Studies/Spring,1988 significance test may then be performed.A more convenient alternative test statistic is given by the ratio of the variances,/: 人=-1 2 V2n,4N(0,2) (7) Although the variance estimator is based on the differences of every other observation,alternative variance estimators may be obtained by using the differences of every gth observation.Suppose that we obtain ng +1 observations X,Xi,...,X,where g is any integer greater than 1.Define the estimators: = x-X-）=(x-x (8a 1n☑e= ng 2（x-X&1- (8b) ng (g=22 (Xe-Xk-g-9驴)2 (8c) ng J(q)≡(q)-品 J(g)= 6(①-1 (8d) G经 The specification test may then be performed using Theorem 1.5 Tbeorem 1.Under the null bypotbesis H,the asymptotic distributions of la(q)andI(q)are given by VnqJaq)4 N(0,2(q-1)00) (9a VngJ(q)a N(0,2(g-1)) (9b Two further refinements of the statistics J and /result in more desirable finite-sample properties.The first is to use overlapping qth differences of X,in estimating the variances by defining the following estimator of 2(X-X-,-9m2 (10) This differs from the estimator (g)since this sum contains nq-g+1 terms,whereas the estimator (g)contains only n terms.By using over- lapping gth increments,we obtain a more efficient estimator and hence a Note that if ()is used to estimate,then the standard t-test of=0 will yield inferences identical to those obtained from the corresponding test of/,=0 for the ratio,since 上-i--5~N0,1) V2V2V2 Proofs of all the theorems are given in the Appendix. 46