Size and Power of Tests for Stationarity in Highly Autocorrelated Time Series
AbstractTests for stationarity are routinely applied to highly persistent time series. Following Kwiatkowski, Phillips, Schmidt and Shin (1992), standard stationarity employs a rescaling by an estimator of the long-run variance of the (potentially) stationary series. This paper analytically investigates the size and power properties of such tests when the series are strongly autocorrelated in a local-to-unity asymptotic framework. It is shown that the behavior of the tests strongly depends on the long-run variance estimator employed, but is in general highly undesirable. Either the tests fail to control for size even for strongly mean reverting series, or they are inconsistent against an integrated process and discriminate only poorly between stationary and integrated processes compared to optimal statistics.
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Bibliographic InfoPaper provided by Department of Economics, University of St. Gallen in its series University of St. Gallen Department of Economics working paper series 2002 with number 2002-26.
Length: 26 pages
Date of creation: Nov 2002
Date of revision:
Tests for stationarity; local-to-unity asymptotics; long-run variance estimation; mean reversion;
Find related papers by 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 &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2003-01-27 (All new papers)
- NEP-ECM-2003-02-10 (Econometrics)
- NEP-ETS-2003-01-27 (Econometric Time Series)
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- Caner, M. & Kilian, L., 2001.
"Size distortions of tests of the null hypothesis of stationarity: evidence and implications for the PPP debate,"
Journal of International Money and Finance,
Elsevier, vol. 20(5), pages 639-657, October.
- Kilian, L. & Caner, M., 1999. "Size Distortions of Tests of the Null Hypothesis of Stationarity: Evidence and Implications for the PPP Debate," Papers 99-05, Michigan - Center for Research on Economic & Social Theory.
- Caner, Mehmet & Kilian, Lutz, 2000. "Size Distortions Of Tests Of The Null Hypothesis Of Stationarity: Evidence And Implications For The PPP Debate," CEPR Discussion Papers 2425, C.E.P.R. Discussion Papers.
- Andrews, Donald W K, 1991.
"Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,"
Econometric Society, vol. 59(3), pages 817-58, May.
- Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
- Lee, Junsoo, 1996. "On the power of stationarity tests using optimal bandwidth estimates," Economics Letters, Elsevier, vol. 51(2), pages 131-137, May.
- Blough, Stephen R, 1992. "The Relationship between Power and Level for Generic Unit Root Tests in Finite Samples," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(3), pages 295-308, July-Sept.
- Ulrich K. Müller & Graham Elliott, 2001. "Tests for Unit Roots and the Initial Observation," University of St. Gallen Department of Economics working paper series 2002 2002-02, Department of Economics, University of St. Gallen.
- Leybourne, S J & McCabe, B P M, 1994. "A Consistent Test for a Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 157-66, April.
- Elliott, Graham, 1999.
"Efficient Tests for a Unit Root When the Initial Observation Is Drawn from Its Unconditional Distribution,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 767-83, August.
- Tom Doan, . "ERSTEST: RATS procedure to perform Elliott-Rothenberg-Stock unit root tests," Statistical Software Components RTS00066, Boston College Department of Economics.
- Donald W.K. Andrews & Christopher J. Monahan, 1990.
"An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator,"
Cowles Foundation Discussion Papers
942, Cowles Foundation for Research in Economics, Yale University.
- Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July.
- Nabeya, Seiji & Tanaka, Katsuto, 1990. "A General Approach to the Limiting Distribution for Estimators in Time Series Regression with Nonstable Autoregressive Errors," Econometrica, Econometric Society, vol. 58(1), pages 145-63, January.
- Shin, Yongcheol, 1994. "A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration," Econometric Theory, Cambridge University Press, vol. 10(01), pages 91-115, March.
- Cochrane, John H., 1991. "A critique of the application of unit root tests," Journal of Economic Dynamics and Control, Elsevier, vol. 15(2), pages 275-284, April.
- Muller, Ulrich & Elliott, Graham, 2001. "Tests for Unit Roots and the Initial Observation," University of California at San Diego, Economics Working Paper Series qt9h99b2sv, Department of Economics, UC San Diego.
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