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On The Asymptotic Power Of The Variance Ratio Test

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  • Deo, Rohit S.
  • Richardson, Matthew

Abstract

The variance-ratio (VR) test statistic, which is based on k-period differences of the data, is commonly used in empirical finance and economics to test the random walk hypothesis. We obtain the asymptotic power function of the VR test statistic when the differencing period k is increasing with the sample size n such that k/n → δ > 0. We show that the test is inconsistent against a variety of mean-reverting alternatives, confirm the result in simulations, and then characterize the functional form of the asymptotic power in terms of δ and these alternatives.

Suggested Citation

  • Deo, Rohit S. & Richardson, Matthew, 2003. "On The Asymptotic Power Of The Variance Ratio Test," Econometric Theory, Cambridge University Press, vol. 19(2), pages 231-239, April.
    • Handle: RePEc:cup:etheor:v:19:y:2003:i:02:p:231-239_19
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    Cited by:

    1. Hiremath, Gourishankar S & Bandi, Kamaiah, 2012. "Variance ratios, structural breaks and nonrandom walk behaviour in the Indian stock returns," MPRA Paper 48710, University Library of Munich, Germany.
    2. Anoop S Kumar, 2011. "Testing for Weak Form of Market Efficiency in Indian Foreign Exchange Market," The IUP Journal of Monetary Economics, IUP Publications, vol. 0(3), pages 7-19, August.
    3. Charles, Amélie & Darné, Olivier, 2009. "The random walk hypothesis for Chinese stock markets: Evidence from variance ratio tests," Economic Systems, Elsevier, vol. 33(2), pages 117-126, June.
    4. Chen, Willa W. & Deo, Rohit S., 2006. "The Variance Ratio Statistic At Large Horizons," Econometric Theory, Cambridge University Press, vol. 22(2), pages 206-234, April.
    5. Madhavi Latha Challa & Venkataramanaiah Malepati & Siva Nageswara Rao Kolusu, 2020. "S&P BSE Sensex and S&P BSE IT return forecasting using ARIMA," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-19, December.
    6. Charles, Amélie & Darné, Olivier, 2009. "The efficiency of the crude oil markets: Evidence from variance ratio tests," Energy Policy, Elsevier, vol. 37(11), pages 4267-4272, November.
    7. Anoop S. KUMAR & Bandi KAMAIAH, 2016. "Efficiency, non-linearity and chaos: evidences from BRICS foreign exchange markets," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(1(606), S), pages 103-118, Spring.
    8. Aye, Goodness C. & Gil-Alana, Luis A. & Gupta, Rangan & Wohar, Mark E., 2017. "The efficiency of the art market: Evidence from variance ratio tests, linear and nonlinear fractional integration approaches," International Review of Economics & Finance, Elsevier, vol. 51(C), pages 283-294.
    9. Amélie Charles & Olivier Darné, 2009. "Variance‐Ratio Tests Of Random Walk: An Overview," Journal of Economic Surveys, Wiley Blackwell, vol. 23(3), pages 503-527, July.
    10. S. Anoop Kumar & Bandi Kamaiah, 2014. "Efficient Market Hypothesis: Some Evidences from Emerging European Forex Markets," Romanian Economic Journal, Department of International Business and Economics from the Academy of Economic Studies Bucharest, vol. 17(52), pages 27-44, June.
    11. Verheyden, Tim & De Moor, Lieven & Van den Bossche, Filip, 2015. "Towards a new framework on efficient markets," Research in International Business and Finance, Elsevier, vol. 34(C), pages 294-308.
    12. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2015. "An investigation into Multivariate Variance Ratio Statistics and their application to Stock Market Predictability," Cambridge Working Papers in Economics 1552, Faculty of Economics, University of Cambridge.
    13. Montagnoli, Alberto & de Vries, Frans P., 2010. "Carbon trading thickness and market efficiency," Energy Economics, Elsevier, vol. 32(6), pages 1331-1336, November.
    14. Simone Bianco & Roberto Ren'o, 2006. "Unexpected volatility and intraday serial correlation," Papers physics/0610023, arXiv.org.
    15. Shyh-wei Chen, 2009. "Random walks in asian foreign exchange markets:evidence from new multiple variance ratio tests," Economics Bulletin, AccessEcon, vol. 29(2), pages 1296-1307.
    16. Hoque, Hafiz A.A.B. & Kim, Jae H. & Pyun, Chong Soo, 2007. "A comparison of variance ratio tests of random walk: A case of Asian emerging stock markets," International Review of Economics & Finance, Elsevier, vol. 16(4), pages 488-502.
    17. Gençay, Ramazan & Signori, Daniele, 2015. "Multi-scale tests for serial correlation," Journal of Econometrics, Elsevier, vol. 184(1), pages 62-80.
    18. Amelie Charles & Olivier Darne, 2009. "Testing for Random Walk Behavior in Euro Exchange Rates," Economie Internationale, CEPII research center, issue 119, pages 25-45.
    19. Deo, Rohit S. & Chen, Willa W., 2003. "The Variance Ratio Statistic at Large Horizons," Papers 2004,04, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    20. Masao Ogaki & Sungwook Park, 2007. "Long-run real exchange rate changes and the properties of the variance of k-differences," Working Papers 07-05, Ohio State University, Department of Economics.
    21. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2015. "An investigation into multivariate variance ratio statistics and their application to stock market predictability," CeMMAP working papers 13/15, Institute for Fiscal Studies.

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