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The Size and Power of the Variance Ratio Test in Finite Samples: A Monte Carlo Investigation

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Author Info
Andrew W. Lo
A. Craig MacKinlay

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Abstract

We examine the finite sample properties of the variance ratio test of the random walk hypothesis via Monte Carlo simulations under two null and three alternative hypotheses. These results are compared to the performance of the Dickey-Fuller t and the Box-Pierce Q statistics. Under the null hypothesis of a random walk with independent and identically distributed Gaussian increments, the empirical size of all three tests are comparable. Under a heteroscedastic random walk null, the variance ratio test is more reliable than either the Dickey-Fuller or Box-Pierce tests. We compute the power of these three tests against three alternatives of recent empirical interest: a stationary AR(1), the sum of this AR(1) and a random walk, and an integrated AR( 1). By choosing the sampling frequency appropriately, the variance ratio test is shown to be as powerful as the Dickey-Fuller and Box-Pierce tests against the stationary alternative, and is more powerful than either of the two tests against the two unit-root alternatives.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0066.

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Date of creation: Jun 1988
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Handle: RePEc:nbr:nberte:0066

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
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  2. Campbell, John Y & Mankiw, N Gregory, 1987. "Are Output Fluctuations Transitory?," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 857-80, November. [Downloadable!] (restricted)
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  3. Shiller, Robert J. & Perron, Pierre, 1985. "Testing the random walk hypothesis : Power versus frequency of observation," Economics Letters, Elsevier, vol. 18(4), pages 381-386. [Downloadable!] (restricted)
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  4. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-61, January. [Downloadable!] (restricted)
  5. Shiller, Robert J, 1981. "The Use of Volatility Measures in Assessing Market Efficiency," Journal of Finance, American Finance Association, vol. 36(2), pages 291-304, May. [Downloadable!] (restricted)
  6. Poterba, James M & Summers, Lawrence H, 1986. "The Persistence of Volatility and Stock Market Fluctuations," American Economic Review, American Economic Association, vol. 76(5), pages 1142-51, December. [Downloadable!] (restricted)
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  7. Robert J. Shiller, 1981. "The Use of Volatility Measures in Assessing Market Efficiency," NBER Working Papers 0565, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  8. Schwert, G. William, 1987. "Effects of model specification on tests for unit roots in macroeconomic data," Journal of Monetary Economics, Elsevier, vol. 20(1), pages 73-103, July. [Downloadable!] (restricted)
  9. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Lo, Andrew W. (Andrew Wen-Chuan) & MacKinlay, Archie Craig, 1955-, 1992. "Maximizing predictability in the stock and bond markets," Working papers 3450-92., Massachusetts Institute of Technology (MIT), Sloan School of Management. [Downloadable!]
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  2. Yuanchen Chang, 2004. "A re-examination of variance-ratio test of random walks in foreign exchange rates," Applied Financial Economics, Taylor and Francis Journals, vol. 14(9), pages 671-679, June. [Downloadable!] (restricted)
  3. Christina Y. Liu & Jia He, 1991. "Do Real Exchange Rates Follow Random Waklks?: A Heteroscedasticity-Robust Autocorrelation Test," International Economic Journal, Korean International Economic Association, vol. 5(3), pages 39-48, October. [Downloadable!] (restricted)
  4. Kaltenbrunner, Annina & Nissanke, Machiko, 2009. "The Case for an Intermediate Exchange Rate Regime with Endogenizing Market Structures and Capital Mobility," Working Papers UNU-WIDER Research Paper , World Institute for Development Economic Research (UNU-WIDER). [Downloadable!]
  5. Jorge Belaire-Franch & Kwaku Opong, 2005. "A Variance Ratio Test of the Behaviour of Some FTSE Equity Indices Using Ranks and Signs," Review of Quantitative Finance and Accounting, Springer, vol. 24(1), pages 93-107, January. [Downloadable!] (restricted)
  6. Paul Eitelman & Justin Vitanza, 2008. "A non-random walk revisited: short- and long-term memory in asset prices," International Finance Discussion Papers 956, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  7. Torben G. Anderson & Tim Bollerslev & Ashish Das, 1998. "Testing for Market Microstructure Effects in Intraday Volatility: A Reassessment of the Tokyo FX Experiment," NBER Working Papers 6666, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  8. Graflund, Andreas, 2000. "A Bayesian Inference Approach to Testing Mean Reversion in the Swedish Stock Market," Working Papers 2000:8, Lund University, Department of Economics, revised 09 Nov 2000. [Downloadable!]
  9. Jose Antonio Ocampo & Maria Angela Parra, 2004. "The Terms Of Trade For Commodities In The Twentieth Century," International Trade 0402006, EconWPA. [Downloadable!]
  10. 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. [Downloadable!] (restricted)
  11. Groenendijk, Patrick A. & Lucas, Andr‚ & Vries, Casper G. de, 1997. "Stochastic processes, non-normal innovations, and the use of scaling ratios," Serie Research Memoranda 0058, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics. [Downloadable!]
  12. Dat Bue Lock, 2007. "The Taiwan stock market does follow a random walk," Economics Bulletin, Economics Bulletin, vol. 7(3), pages 1-8. [Downloadable!]
  13. Yihui Lan, 2001. "The Long-Run Value of Currencies: A Big Mac Perspective," Economics Discussion / Working Papers 01-17, The University of Western Australia, Department of Economics. [Downloadable!]
  14. José Carlos Dias & Luís Lopes & Vitor Martins & José Manuel Benzinho, 2004. "Efficiency tests in the Iberian stock markets," Finance 0406001, EconWPA. [Downloadable!]
  15. 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. [Downloadable!]
  16. Eduardo Jose Araújo Lima & Benjamin Miranda Tabak, 2004. "Tests of the random walk hypothesis for equity markets: evidence from China, Hong Kong and Singapore," Applied Economics Letters, Taylor and Francis Journals, vol. 11(4), pages 255-258, March. [Downloadable!] (restricted)
  17. Francis W. Ahking, 2004. "Non-Parametric Tests of Real Exchange rates in the Post-Bretton Woods Era," Working papers 2004-05, University of Connecticut, Department of Economics. [Downloadable!]
  18. Willa Chen & Rohit Deo, 2005. "The Variance Ratio Statistic at large Horizons," Econometrics 0501003, EconWPA. [Downloadable!]
    Other versions:
  19. Simone Bianco & Roberto Ren\'o, 2006. "Unexpected volatility and intraday serial correlation," Quantitative Finance Papers physics/0610023, arXiv.org. [Downloadable!]
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