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Unit root quantile autoregression testing using covariates

  • Galvao Jr., Antonio F.
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    This paper extends unit root tests based on quantile regression proposed by Koenker and Xiao [Koenker, R., Xiao, Z., 2004. Unit root quantile autoregression inference, Journal of the American Statistical Association 99, 775-787] to allow stationary covariates and a linear time trend. The limiting distribution of the test is a convex combination of Dickey-Fuller and standard normal distributions, with weight determined by the correlation between the equation error and the regression covariates. A simulation experiment is described, illustrating the finite sample performance of the unit root test for several types of distributions. The test based on quantile autoregression turns out to be especially advantageous when innovations are heavy-tailed. An application to the CPI-based real exchange rates using four different countries suggests that real exchange rates are not constant unit root processes.

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    File URL: http://www.sciencedirect.com/science/article/B6VC0-4VCWG8D-1/2/bed867f126954fc4e04be0e3384b6a92
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    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 152 (2009)
    Issue (Month): 2 (October)
    Pages: 165-178

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    Handle: RePEc:eee:econom:v:152:y:2009:i:2:p:165-178
    Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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    1. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-72, July.
    2. Maurice Obstfeld & Kenneth Rogoff, 2000. "The Six Major Puzzles in International Macroeconomics: Is There a Common Cause?," NBER Working Papers 7777, National Bureau of Economic Research, Inc.
    3. Seo, Byeongseon, 1999. "Distribution theory for unit root tests with conditional heteroskedasticity1," Journal of Econometrics, Elsevier, vol. 91(1), pages 113-144, July.
    4. Elena Pesavento, 2006. "Near-Optimal Unit Root Tests with Stationary Covariates with Better Finite Sample Size," Economics Working Papers ECO2006/18, European University Institute.
    5. Thompson, Samuel B., 2004. "Robust Tests Of The Unit Root Hypothesis Should Not Be," Econometric Theory, Cambridge University Press, vol. 20(02), pages 360-381, April.
    6. Qu, Zhongjun, 2008. "Testing for structural change in regression quantiles," Journal of Econometrics, Elsevier, vol. 146(1), pages 170-184, September.
    7. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
    8. Graham Elliott & Michael Jansson, . "Testing for Unit Roots with Stationary Covariates," Economics Working Papers 2000-6, School of Economics and Management, University of Aarhus.
    9. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    10. Machado, José A.F., 1993. "Robust Model Selection and M-Estimation," Econometric Theory, Cambridge University Press, vol. 9(03), pages 478-493, June.
    11. Su, Liangjun & Xiao, Zhijie, 2008. "Testing for parameter stability in quantile regression models," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2768-2775, November.
    12. Elliott, Graham & Pesavento, Elena, 2006. "On the Failure of Purchasing Power Parity for Bilateral Exchange Rates after 1973," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(6), pages 1405-1430, September.
    13. Shin, Dong Wan & So, Beong Soo, 1999. "Unit Root Tests Based On Adaptive Maximum Likelihood Estimation," Econometric Theory, Cambridge University Press, vol. 15(01), pages 1-23, February.
    14. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
    15. Peter C.B. Phillips, 1993. "Fully Modified Least Squares and Vector Autoregression," Cowles Foundation Discussion Papers 1047, Cowles Foundation for Research in Economics, Yale University.
    16. Hansen, Bruce E., 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1148-1171, October.
    17. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
    18. Hasan, Mohammad N., 2001. "Rank tests of unit root hypothesis with infinite variance errors," Journal of Econometrics, Elsevier, vol. 104(1), pages 49-65, August.
    19. Rothenberg, Thomas J. & Stock, James H., 1997. "Inference in a nearly integrated autoregressive model with nonnormal innovations," Journal of Econometrics, Elsevier, vol. 80(2), pages 269-286, October.
    20. Lucas, André, 1995. "Unit Root Tests Based on M Estimators," Econometric Theory, Cambridge University Press, vol. 11(02), pages 331-346, February.
    21. Knight, Keith, 1991. "Limit Theory for M-Estimates in an Integrated Infinite Variance," Econometric Theory, Cambridge University Press, vol. 7(02), pages 200-212, June.
    22. Roger Koenker & Zhijie Xiao, 2004. "Unit Root Quantile Autoregression Inference," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 775-787, January.
    23. M. N. Hasan & R. W. Koenker, 1997. "Robust Rank Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 65(1), pages 133-162, January.
    24. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 99-125, January.
    25. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    26. Michael, Panos & Nobay, A Robert & Peel, David A, 1997. "Transactions Costs and Nonlinear Adjustment in Real Exchange Rates: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 862-79, August.
    27. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 1," Cowles Foundation Discussion Papers 811R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1987.
    28. 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.
    29. Papell, David H., 1997. "Searching for stationarity: Purchasing power parity under the current float," Journal of International Economics, Elsevier, vol. 43(3-4), pages 313-332, November.
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