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Optimal Power for Testing Potential Cointegrating Vectors with Known

  • Elliott, Graham
  • Jansson, Michael
  • Pesavento, Elena

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 qt2bv7n071.

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Date of creation: 01 Jun 2004
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Handle: RePEc:cdl:ucsdec:qt2bv7n071
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  1. Vogelsang, T.I. & Perron, P., 1991. "Nonstationary and Level Shifts With An Application To Purchasing Power Parity," Papers 359, Princeton, Department of Economics - Econometric Research Program.
  2. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. Bernard, A.B. & Durlauf, S.N., 1993. "Convergence in International Output," Working papers 93-7, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. 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.
  10. Graham Elliott & Michael Jansson, . "Testing for Unit Roots with Stationary Covariates," Economics Working Papers 2000-6, School of Economics and Management, University of Aarhus.
  11. 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.
  12. Aggarwal, Raj & Mohanty, Sunil & Song, Frank, 1995. "Are Survey Forecasts of Macroeconomic Variables Rational?," The Journal of Business, University of Chicago Press, vol. 68(1), pages 99-119, January.
  13. 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.
  14. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, March.
  15. 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.
  16. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  17. 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.
  18. 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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