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Exact Non-Parametric Tests for a Random Walk with Unknown Drift under Conditional Heteroscedasticity

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  • Luger, Richard

Abstract

This paper proposes a class of linear signed rank statistics to test for a random walk with unknown drift in the presence of arbitrary forms of conditional heteroscedasticity. The class considered includes analogues of the well-known sign and Wilcoxon test statistics. The exactness of the proposed tests rests only on the assumption that the errors are symmetrically distributed. No other assumptions, such as normality or even the existence of moments, are required. Simulations confirm the reliability of the proposed tests, and their power is superior to that of the parametric variance-ratio test. The inference methods developed are illustrated by a test of the random walk hypothesis in exchange rates for five major currencies against the U.S. dollar.

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Bibliographic Info

Paper provided by Bank of Canada in its series Working Papers with number 01-2.

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Length: 35 pages
Date of creation: 2001
Date of revision:
Handle: RePEc:bca:bocawp:01-2

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Keywords: Econometric and statistical methods;

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Citations

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Cited by:
  1. 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.
  2. Belaire-Franch, Jorge & Opong, Kwaku K., 2005. "Some evidence of random walk behavior of Euro exchange rates using ranks and signs," Journal of Banking & Finance, Elsevier, vol. 29(7), pages 1631-1643, July.
  3. David McMillan & Pako Thupayagale, 2011. "Measuring volatility persistence and long memory in the presence of structural breaks: Evidence from African stock markets," Managerial Finance, Emerald Group Publishing, vol. 37(3), pages 219-241, March.
  4. Amélie Charles & Olivier Darne, 2009. "Variance ratio tests of random walk: An overview," Post-Print hal-00771078, HAL.
  5. Marc Hallin & Ramon van den Akker & Bas J.M. Werker, 2011. "A class of simple distribution-free rank-based unit root tests," Post-Print hal-00834424, HAL.
  6. Hung, Jui-Cheng, 2009. "Deregulation and liberalization of the Chinese stock market and the improvement of market efficiency," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(3), pages 843-857, August.
  7. Collins G. Ntim & Kwaku K. Opong & Jo Danbolt & Frank Senyo Dewotor, 2011. "Testing the weak-form efficiency in African stock markets," Managerial Finance, Emerald Group Publishing, vol. 37(3), pages 195-218, March.
  8. Jorge Belaire-Franch & Kwaku Opong, 2013. "A Time Series Analysis of U.K. Construction and Real Estate Indices," The Journal of Real Estate Finance and Economics, Springer, vol. 46(3), pages 516-542, April.
  9. Gungor, Sermin & Luger, Richard, 2009. "Exact distribution-free tests of mean-variance efficiency," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 816-829, December.
  10. Marc Hallin & Ramon van den Akker & Bas Werker, 2009. "A class of Simple Semiparametrically Efficient Rank-Based Unit Root Tests," Working Papers ECARES 2009_001, ULB -- Universite Libre de Bruxelles.
  11. Paulo M.M. Rodrigues & Antonio Rubia, 2004. "On The Small Sample Properties Of Dickey Fuller And Maximum Likelihood Unit Root Tests On Discrete-Sampled Short-Term Interest Rates," Working Papers. Serie AD 2004-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  12. Mobarek, Asma & Fiorante, Angelo, 2014. "The prospects of BRIC countries: Testing weak-form market efficiency," Research in International Business and Finance, Elsevier, vol. 30(C), pages 217-232.

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