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Unit Root Testing with Stationary Covariates and a Structural Break in the Trend Function

The issue of testing for a unit root allowing for a structural break in the trend function is considered. The focus is on the construction of more powerful tests using the information in relevant multivariate data sets. The proposed test adopts the GLS detrending approach and uses correlated stationary covariates to improve power. As it is standard in the literature, the break date is treated as unknown. Asymptotic distributions are derived and a set of asymptotic and nite sample critical values are tabulated. Asymptotic local power functions show that power gains can be large. Finite sample results show that the test exhibits small size distortions and power that can be far beyond what is achievable by univariate tests.

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Paper provided by University of Alberta, Department of Economics in its series Working Papers with number 2011-10.

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Length: 49 pages
Date of creation: 01 May 2011
Date of revision:
Handle: RePEc:ris:albaec:2011_010
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  1. Harris, David & Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Testing For A Unit Root In The Presence Of A Possible Break In Trend," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1545-1588, December.
  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. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  4. Fossati, Sebastian, 2012. "Covariate unit root tests with good size and power," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3070-3079.
  5. Bruce E. Hansen, 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Boston College Working Papers in Economics 300., Boston College Department of Economics.
  6. Glenn D. Rudebusch, 1992. "The uncertain unit root in real GNP," Finance and Economics Discussion Series 193, Board of Governors of the Federal Reserve System (U.S.).
  7. Graham Elliott & Michael Jansson, . "Testing for Unit Roots with Stationary Covariates," Economics Working Papers 2000-6, School of Economics and Management, University of Aarhus.
  8. Carrion-i-Silvestre, Josep Lluís & Kim, Dukpa & Perron, Pierre, 2009. "Gls-Based Unit Root Tests With Multiple Structural Breaks Under Both The Null And The Alternative Hypotheses," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1754-1792, December.
  9. Perron, Pierre, 1997. "Further evidence on breaking trend functions in macroeconomic variables," Journal of Econometrics, Elsevier, vol. 80(2), pages 355-385, October.
  10. Vogelsang, Timothy J & Perron, Pierre, 1998. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1073-1100, November.
  11. Giuseppe Cavaliere & David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2009. "Testing for unit roots in the presence of a possible break in trend and non-stationary volatility," Discussion Papers 09/05, University of Nottingham, Granger Centre for Time Series Econometrics.
  12. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
  13. Elena Pesavento, 2006. "Near-Optimal Unit Root Tests with Stationary Covariates with Better Finite Sample Size," Economics Working Papers ECO2006/18, European University Institute.
  14. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
  15. Mohitosh Kejriwal & Pierre Perron, 2006. "Unit Root Tests Allowing for a Break in the Trend Function at an Unknown Time Under Both the Null and Alternative Hypotheses," Boston University - Department of Economics - Working Papers Series WP2006-052, Boston University - Department of Economics.
  16. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
  17. Papell, David H & Prodan, Ruxandra, 2004. "The Uncertain Unit Root in U.S. Real GDP: Evidence with Restricted and Unrestricted Structural Change," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(3), pages 423-27, June.
  18. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  19. Juhl, Ted & Xiao, Zhijie, 2003. "Power Functions And Envelopes For Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(02), pages 240-253, April.
  20. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  21. Gabriel Rodriguez, 2006. "Finite Sample Behaviour of the Level Shift Model using Quasi-Differenced Data," Working Papers 0604E, University of Ottawa, Department of Economics.
  22. David H Papell & Ruxandra Prodan, 2007. "Restricted Structural Change And The Unit Root Hypothesis," Economic Inquiry, Western Economic Association International, vol. 45(4), pages 834-853, October.
  23. Caporale, Guglielmo Maria & Pittis, Nikitas, 1999. " Unit Root Testing Using Covariates: Some Theory and Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(4), pages 583-95, November.
  24. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.
  25. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  26. Christiano, Lawrence J, 1992. "Searching for a Break in GNP," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 237-50, July.
  27. Robin L. Lumsdaine & David H. Papell, 1997. "Multiple Trend Breaks And The Unit-Root Hypothesis," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 212-218, May.
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