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."> 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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The Variance Ratio Statistic at large Horizons

Author

Listed:
  • Willa Chen

    (Texas A&M University)

  • Rohit Deo

    (New york University)

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 → δ >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.

Suggested Citation

  • Willa Chen & Rohit Deo, 2005. "The Variance Ratio Statistic at large Horizons," Econometrics 0501003, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0501003
    Note: Type of Document - pdf; pages: 40
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    References listed on IDEAS

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    6. Willa W. Chen & Rohit S. Deo, 2004. "Power transformations to induce normality and their applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 117-130, February.
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    More about this item

    Keywords

    Mean reversion; frequency domain; power transformations;
    All these keywords.

    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; Diffusion Processes

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