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Optimal Power for Testing Potential Cointegrating Vectors with Known

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Author Info
Graham Elliott (University of California, San Diego)
Michael Jansson (University of California, Berkeley)
Elena Pesavento (Emory University)

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Abstract

Theory often specifies a particular cointegrating vector amongst integrated variables and it is often required that one test for a unit root in the known cointegrating vector. It is common to simply employ a univariate test for a unit root, but this does not take into account all available information. We show that in such testing situations, a family of tests with optimality properties exists. We use this to characterize the extent of the loss in power from using popular methods, as well as to derive a test that works well in practice. We characterize the extent of the losses of not imposing the cointegrating vector in the testing procedure. We apply various tests to the hypothesis that price forecasts from the Livingston data survey are cointegrated with prices, and find that although most tests fail to reject the presence of a unit root in forecast errors the tests presented here strongly reject this (implausible) hypothesis.

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Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number 2004-08.

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Date of creation: 29 Sep 2004
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Handle: RePEc:cdl:ucsdec:2004-08

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Keywords: Cointegration; optimal test; unit roots;

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  2. Peter Boswijk, H., 1994. "Testing for an unstable root in conditional and structural error correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 37-60, July. [Downloadable!] (restricted)
  3. repec:cup:etheor:v:11:y:1995:i:5:p:984-1014 is not listed on IDEAS
  4. Pesavento, Elena, 2004. "Analytical evaluation of the power of tests for the absence of cointegration," Journal of Econometrics, Elsevier, vol. 122(2), pages 349-384, October. [Downloadable!] (restricted)
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  5. Aggarwal, Raj & Mohanty, Sunil & Song, Frank, 1995. "Are Survey Forecasts of Macroeconomic Variables Rational?," Journal of Business, University of Chicago Press, vol. 68(1), pages 99-119, January. [Downloadable!] (restricted)
  6. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
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  7. repec:cup:etheor:v:11:y:1995:i:5:p:1148-71 is not listed on IDEAS
  8. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
  9. Liu, Peter C. & Maddala, G. S., 1992. "Rationality of survey data and tests for market efficiency in the foreign exchange markets," Journal of International Money and Finance, Elsevier, vol. 11(4), pages 366-381, August. [Downloadable!] (restricted)
  10. 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. [Downloadable!]
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  11. Banerjee, Anindya, et al, 1986. "Exploring Equilibrium Relationships in Econometrics through Static Models: Some Monte Carlo Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 253-77, August.
  12. Eric Zivot, 1996. "The Power of Single Equation Tests for Cointegration when the Cointegrating Vector is Prespecified," Econometrics 9612001, EconWPA. [Downloadable!]
  13. Graham Elliott & Michael Jansson, . "Testing for Unit Roots with Stationary Covariates," Economics Working Papers 2000-6, School of Economics and Management, University of Aarhus. [Downloadable!]
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  14. Cheung, Yin-Wong & Lai, Kon S., 1999. "On Cross-Country Differences in the Persistence of Real Exchange Rates," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
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  15. Greasley, David & Oxley, Les, 1997. "Time-series based tests of the convergence hypothesis: Some positive results," Economics Letters, Elsevier, vol. 56(2), pages 143-147, October. [Downloadable!] (restricted)
  16. Perron, Pierre & Vogelsang, Timothy J, 1992. "Nonstationarity and Level Shifts with an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 301-20, July.
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  17. Bernard, Andrew B & Durlauf, Steven N, 1995. "Convergence in International Output," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 97-108, April-Jun. [Downloadable!] (restricted)
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  18. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254. [Downloadable!] (restricted)
  19. Horvath, Michael T.K. & Watson, Mark W., 1995. "Testing for Cointegration When Some of the Cointegrating Vectors are Prespecified," Econometric Theory, Cambridge University Press, vol. 11(05), pages 984-1014, October. [Downloadable!]
  20. Harbo, Ingrid, et al, 1998. "Asymptotic Inference on Cointegrating Rank in Partial Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 388-99, October.
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