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Asymptotic Theory of LAD Estimation in a Unit Root Process with Finite Variance Errors

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  • Herce, Miguel A.

Abstract

In this paper we derive the asymptotic distribution of the least absolute deviations ( LAD ) estimator of the autoregressive parameter under the unit root hypothesis, when the errors are assumed to have finite variances, and present LAD -based unit root tests, which, under heavy-tailed errors, are expected to be more powerful than tests based on least squares. The limiting distribution of the LAD estimator is that of a functional of a bivariate Brownian motion, similar to those encountered in cointegrating regressions. By appropriately correcting for serial correlation and other distributional parameters, the test statistics introduced here are found to have either conditional or unconditional normal limiting distributions. The results of the paper complement similar ones obtained by Knight (1991, Canadian Journal of Statistics 17, 261-278) for infinite variance errors. A simulation study is conducted to investigate the finite sample properties of our tests.

Suggested Citation

  • Herce, Miguel A., 1996. "Asymptotic Theory of LAD Estimation in a Unit Root Process with Finite Variance Errors," Econometric Theory, Cambridge University Press, vol. 12(01), pages 129-153, March.
  • Handle: RePEc:cup:etheor:v:12:y:1996:i:01:p:129-153_00
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    Cited by:

    1. So, Beong Soo & Shin, Dong Wan, 2001. "An invariant sign test for random walks based on recursive median adjustment," Journal of Econometrics, Elsevier, vol. 102(2), pages 197-229, June.
    2. Galvao Jr., Antonio F., 2009. "Unit root quantile autoregression testing using covariates," Journal of Econometrics, Elsevier, vol. 152(2), pages 165-178, October.
    3. Avdoulas, Christos & Bekiros, Stelios & Boubaker, Sabri, 2016. "Detecting nonlinear dependencies in eurozone peripheral equity markets: A multistep filtering approach," Economic Modelling, Elsevier, vol. 58(C), pages 580-587.
    4. Uwe Hassler & Paulo M.M. Rodrigues & Antonio Rubia, 2016. "Quantile Regression for Long Memory Testing: A Case of Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(4), pages 693-724.
    5. Zhou, Zhiyong & Lin, Zhengyan, 2014. "Asymptotic theory for LAD estimation of moderate deviations from a unit root," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 25-32.
    6. Narayan, Paresh Kumar & Liu, Ruipeng & Westerlund, Joakim, 2016. "A GARCH model for testing market efficiency," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 41(C), pages 121-138.
    7. Rickard Sandberg, 2015. "M-estimator based unit root tests in the ESTAR framework," Statistical Papers, Springer, vol. 56(4), pages 1115-1135, November.
    8. Michael Jansson, 2008. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 76(5), pages 1103-1142, September.
    9. Kai Carstensen, 2003. "The finite-sample performance of robust unit root tests," Statistical Papers, Springer, vol. 44(4), pages 469-482, October.
    10. W. K. Li & Shiqing Ling & Michael McAleer, 2001. "A Survey of Recent Theoretical Results for Time Series Models with GARCH Errors," ISER Discussion Paper 0545, Institute of Social and Economic Research, Osaka University.
    11. Zernov, Serguei & Zinde-Walsh, Victoria & Galbraith, John W., 2009. "Asymptotics for estimation of quantile regressions with truncated infinite-dimensional processes," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 497-508, March.
    12. repec:bla:jtsera:v:38:y:2017:i:6:p:1000-1009 is not listed on IDEAS
    13. Moreno, Marta & Romo, Juan, 1997. "Bootstrap tests for unit roots based on lad estimation," DES - Working Papers. Statistics and Econometrics. WS 6210, Universidad Carlos III de Madrid. Departamento de Estadística.
    14. Ling, Shiqing & McAleer, Michael, 2004. "Regression quantiles for unstable autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 304-328, May.
    15. Shin, Dong Wan & Park, Soo Jung & Oh, Man-Suk, 2009. "A robust sign test for panel unit roots under cross sectional dependence," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1312-1327, February.
    16. Shin, Dong Wan & Park, Sangun, 2010. "Robust panel unit root tests for cross-sectionally dependent multiple time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2801-2813, November.
    17. Shin, Dong Wan & So, Beong Soo, 1999. "New tests for unit roots in autoregressive processes with possibly infinite variance errors," Statistics & Probability Letters, Elsevier, vol. 44(4), pages 387-397, October.
    18. Serguei Zernov & Victoria Zindle-Walsh & John Galbraith, 2006. "Asymptotics For Estimation Of Truncated Infinite-Dimensional Quantile Regressions," Departmental Working Papers 2006-16, McGill University, Department of Economics.
    19. Horowitz, Joel L. & Savin, N. E., 2000. "Empirically relevant critical values for hypothesis tests: A bootstrap approach," Journal of Econometrics, Elsevier, vol. 95(2), pages 375-389, April.
    20. Furno, Marilena, 2001. "LAD estimation with random coefficient autocorrelated errors," Computational Statistics & Data Analysis, Elsevier, vol. 36(4), pages 511-523, June.
    21. Guodong Li & Chenlei Leng & Chih-Ling Tsai, 2014. "A Hybrid Bootstrap Approach To Unit Root Tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 299-321, July.
    22. White, Halbert & Kim, Tae-Hwan, 2002. "Estimation, Inference, and Specification Testing for Possibly Misspecified Quantile Regression," University of California at San Diego, Economics Working Paper Series qt1s38s0dn, Department of Economics, UC San Diego.

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