The Variance Ratio Statistic at Large Horizons
AbstractWe 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. --
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Bibliographic InfoPaper provided by Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE) in its series Papers with number 2004,04.
Date of creation: 2003
Date of revision:
Mean reversion; Frequency domain; Power transformation;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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