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Title:The Variance Ratio Statistic at Large Horizons PDF Logo
Authors:Deo, Rohit S.
Chen, Willa W.
Issue Date:2003
Series/Report no.:Papers / Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE) 2004,04
Abstract:We make three contributions to using the variance ratio statistic at large horizons. Allowing for general heteroscedasticity in the data, we obtain the asymptotic distribution of the statistic when the horizon k is increasing with the sample size n but at a slower rate so that k=n ! 0. The test is shown to be consistent against a variety of relevant mean reverting alternatives when k=n ! 0. This is in contrast to the case when k=n ! – > 0; where the statistic has been recently shown to be inconsistent against such alternatives. Secondly, we provide and justify a simple power transformation of the statistic which yields almost perfectly normally distributed statistics in finite samples, solving the well known right skewness problem. Thirdly, we provide a more powerful way of pooling information from different horizons to test for mean reverting alternatives. Monte Carlo simulations illustrate the theoretical improvements provided.
Subjects:Mean reversion
Frequency domain
Power transformation
JEL:C12
C22
Document Type:Working Paper
Appears in Collections:Papers, CASE - Center for Applied Statistics and Economics, HU Berlin

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