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|Title:||The Variance Ratio Statistic at Large Horizons |
|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.|
|Document Type:||Working Paper|
|Appears in Collections:||Papers, CASE - Center for Applied Statistics and Economics, HU Berlin|
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