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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.

Suggested Citation

  • Luger, Richard, 2001. "Exact Non-Parametric Tests for a Random Walk with Unknown Drift under Conditional Heteroscedasticity," Staff Working Papers 01-2, Bank of Canada.
  • Handle: RePEc:bca:bocawp:01-2
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    Cited by:

    1. 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.
    2. repec:hal:journl:peer-00834424 is not listed on IDEAS
    3. Hallin, M. & van den Akker, R. & Werker, B.J.M., 2011. "A Class of Simple Distribution-free Rank-based Unit Root Tests (Revision of DP 2010-72)," Discussion Paper 2011-002, Tilburg University, Center for Economic Research.
    4. 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.
    5. 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.
    6. Arjoon, Vaalmikki, 2016. "Microstructures, financial reforms and informational efficiency in an emerging market," Research in International Business and Finance, Elsevier, vol. 36(C), pages 112-126.
    7. Hallin, Marc & van den Akker, Ramon & Werker, Bas J.M., 2011. "A class of simple distribution-free rank-based unit root tests," Journal of Econometrics, Elsevier, vol. 163(2), pages 200-214, August.
    8. 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.
    9. 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).
    10. 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.
    11. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2014. "Multivariate Variance Ratio Statistics," Cambridge Working Papers in Economics 1459, Faculty of Economics, University of Cambridge.
    12. 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, February.
    13. 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 CWP13/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. 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.
    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. 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, February.
    17. 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.
    18. Ntim, Collins G. & English, John & Nwachukwu, Jacinta & Wang, Yan, 2015. "On the efficiency of the global gold markets," International Review of Financial Analysis, Elsevier, vol. 41(C), pages 218-236.

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    Keywords

    Econometric and statistical methods;

    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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