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The Variance Ratio Statistic At Large Horizons

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  • Chen, Willa W.
  • Deo, Rohit S.

Abstract

We make three contributions to using the variance ratio statistic at large horizons. Allowing for general heteroskedasticity 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. Second, we provide and justify a simple power transformation of the statistic that yields almost perfectly normally distributed statistics in finite samples, solving the well-known right skewness problem. Third, 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.The authors thank Bruce Hansen and the referees for useful suggestions and comments that greatly improved the paper. The first author s research was supported by NSF grant DMS-0306726.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 22 (2006)
Issue (Month): 02 (April)
Pages: 206-234

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Handle: RePEc:cup:etheor:v:22:y:2006:i:02:p:206-234_06

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  1. Andrew W. Lo & Craig A. MacKinlay, . "The Size and Power of the Variance Ratio Test in Finite Samples: A Monte Carlo Investigation," Rodney L. White Center for Financial Research Working Papers 28-87, Wharton School Rodney L. White Center for Financial Research.
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  3. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  4. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
  5. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-73, April.
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  7. Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
  8. Deo, Rohit S. & Richardson, Matthew, 2003. "On The Asymptotic Power Of The Variance Ratio Test," Econometric Theory, Cambridge University Press, vol. 19(02), pages 231-239, April.
  9. Matthew Richardson & James H. Stock, 1990. "Drawing Inferences From Statistics Based on Multi-Year Asset Returns," NBER Working Papers 3335, National Bureau of Economic Research, Inc.
  10. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  11. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
  12. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
  13. Faust, Jon, 1992. "When Are Variance Ratio Tests for Serial Dependence Optimal?," Econometrica, Econometric Society, vol. 60(5), pages 1215-26, September.
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Cited by:
  1. Amélie Charles & Olivier Darne, 2009. "Variance ratio tests of random walk: An overview," Post-Print hal-00771078, HAL.
  2. Righi, Marcelo Brutti & Ceretta, Paulo Sergio, 2013. "Risk prediction management and weak form market efficiency in Eurozone financial crisis," International Review of Financial Analysis, Elsevier, vol. 30(C), pages 384-393.
  3. Kim, Jae H., 2009. "Automatic variance ratio test under conditional heteroskedasticity," Finance Research Letters, Elsevier, vol. 6(3), pages 179-185, September.
  4. Peter C.B. Phillips & Sainan Jin, 2013. "Testing the Martingale Hypothesis," Cowles Foundation Discussion Papers 1912, Cowles Foundation for Research in Economics, Yale University.
  5. Amélie Charles & Olivier Darné & Jae H. Kim, 2010. "Exchange-Rate Return Predictability and the Adaptive Markets Hypothesis: Evidence from Major Foreign Exchange Rates," Working Papers hal-00547722, HAL.
  6. Chen, Min & Zhu, Ke, 2014. "Sign-based specification tests for martingale difference with conditional heteroscedasity," MPRA Paper 56347, University Library of Munich, Germany.
  7. Sasikumar, Anoop, 2011. "Testing for weak form market efficiency in Indian foreign exchange market," MPRA Paper 37071, University Library of Munich, Germany.
  8. Amélie Charles & Olivier Darné & Jessica Fouilloux, 2010. "Testing the Martingale Difference Hypothesis in the EU ETS Markets for the CO2 Emission Allowances: Evidence from Phase I and Phase II," Working Papers hal-00473727, HAL.
  9. Amelie Charles & Olivier Darne, 2009. "Testing for Random Walk Behavior in Euro Exchange Rates," Economie Internationale, CEPII research center, issue 119, pages 25-45.

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