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Weighted symmetric tests for a unit root: response functions, power, test dependence and test conflict

  • K. Patterson
  • Saeed Heravi
Registered author(s):

    The most frequently applied test statistics for a unit root are the Dickey-Fuller tests, which are built into many econometric packages along with MacKinnon's empirical response functions. This article provides empirical response functions for some easy to compute alternative test statistics that are generally much more powerful than the Dickey-Fuller tests; specifically, these are the Dickey-Fuller tests and the weighted symmetric versions of the and tests. The empirical response functions presented here take into account adjustments for lag length in the maintained regression, and also extend the design of the simulation experiments compared to previous work. A second aspect of this study concerns the widespread practice in applied econometrics of using more than one test for the same feature without an assessment of the implications for the cumulative significance level and probability of test conflict. Tests for a unit root being are a leading example of this practice. Using the extended set of unit root tests considered here, the extent of test dependence is simulated and overall type one error calculated. Two empirical applications illustrate the key principles.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/0003684022000030372
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    Article provided by Taylor & Francis Journals in its journal Applied Economics.

    Volume (Year): 35 (2003)
    Issue (Month): 7 ()
    Pages: 779-790

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    Handle: RePEc:taf:applec:v:35:y:2003:i:7:p:779-790
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    1. Chris Murray & Charles Nelson, 1998. "The Uncertain Trend in U.S. GDP," Discussion Papers in Economics at the University of Washington 0074, Department of Economics at the University of Washington.
    2. Sarno, Lucio & Taylor, Mark P, 1997. "The Behaviour of Real Exchange Rates During the Post-Bretton Woods Period," CEPR Discussion Papers 1730, C.E.P.R. Discussion Papers.
    3. West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
    4. 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.
    5. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
    6. Hylleberg, Svend & Mizon, Grayham E., 1989. "A note on the distribution of the least squares estimator of a random walk with drift," Economics Letters, Elsevier, vol. 29(3), pages 225-230.
    7. K. D. Patterson & S. M. Heravi, 2003. "The impact of fat-tailed distributions on some leading unit roots tests," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(6), pages 635-667.
    8. Pantula, Sastry G & Gonzalez-Farias, Graciela & Fuller, Wayne A, 1994. "A Comparison of Unit-Root Test Criteria," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 449-59, October.
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