Optimal Power For Testing Potential Cointegrating Vectors with Known Parameters for Nonstationarity

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Optimal Power For Testing Potential Cointegrating Vectors with Known Parameters for Nonstationarity

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Graham Elliott
Michael Jansson
Elena Pesavento ()

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Abstract

In situations where theory specifies a potential cointegrating vector amongst integrated variables, it is often required that one test for a unit root in the constructed cointegrating vector. Although it is common to simply employ a univariate test for a unit root for this test, it is known that this does not take into account all available information. We show here 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 also 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, Emory University (Atlanta) in its series Emory Economics with number 0303.

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Date of creation: Feb 2003
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Handle: RePEc:emo:wp2003:0303

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Article
- Graham Elliott & Michael Jansson & Elena Pesavento, 2005. "Optimal Power for Testing Potential Cointegrating Vectors With Known Parameters for Nonstationarity," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 34-48, January. [Downloadable!] (restricted)

This paper has been announced in the following NEP Reports:

NEP-ALL-2003-06-04 (All new papers)
NEP-ECM-2003-06-09 (Econometrics)
NEP-ETS-2003-06-04 (Econometric Time Series)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
Other versions:
- Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation, Yale University, revised Sep 1987. [Downloadable!]
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)
repec:cup:etheor:v:11:y:1995:i:5:p:984-1014 is not listed on IDEAS
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)
Other versions:
- Elena Pesavento, 2000. "Analytical Evaluation of the Power of Tests for the Absence of Cointegration," University of California at San Diego, Economics Working Paper Series 2000-24, Department of Economics, UC San Diego. [Downloadable!]
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)
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.
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Other versions:
- Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation, Yale University. [Downloadable!]
Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March. [Downloadable!] (restricted)
Graham Elliott & Michael Jansson, 2000. "Testing for Unit Roots with Stationary Covariances," University of California at San Diego, Economics Working Paper Series 2000-06, Department of Economics, UC San Diego. [Downloadable!]
Other versions:
- 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!]
- Graham Elliott & Michael Jansson, 2002. "Testing for Unit Roots with Stationary Covariates," University of California at San Diego, Economics Working Paper Series 2000-06r, Department of Economics, UC San Diego. [Downloadable!]
- Elliott, Graham & Jansson, Michael, 2003. "Testing for unit roots with stationary covariates," Journal of Econometrics, Elsevier, vol. 115(1), pages 75-89, July. [Downloadable!] (restricted)
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!]
Other versions:
- Cheung, Yin-Wong & Lai, Kon S., 2000. "On cross-country differences in the persistence of real exchange rates," Journal of International Economics, Elsevier, vol. 50(2), pages 375-397, April. [Downloadable!] (restricted)
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Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July. [Downloadable!] (restricted)
Other versions:
- 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. [Downloadable!] (restricted)
Yin-Wong Cheung & Menzie D. Chinn, 1999. "Are Macroeconomic Forecasts Informative? Cointegration Evidence from the ASA-NBER Surveys," NBER Working Papers 6926, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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.
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)
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)
Other versions:
- Bernard, A.B. & Durlauf, S.N., 1993. "Convergence in International Output," Working papers 93-7, Massachusetts Institute of Technology (MIT), Department of Economics.
Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254. [Downloadable!] (restricted)
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!]

Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Elena Pesavento, 2006. "Near-Optimal Unit Root Tests with Stationary Covariates with Better Finite Sample Size," Economics Working Papers ECO2006/18, European University Institute. [Downloadable!]
Other versions:
- Elena Pesavento, 2006. "Near-Optimal Unit Root Test with Stationary Covariate with Better Finite Sample Size," Emory Economics 0606, Department of Economics, Emory University (Atlanta). [Downloadable!]
Elena Pesavento & Barbara Rossi, 2004. "Do Technology Shocks Drive Hours Up or Down? A Little Evidence From an Agnostic Procedure," Econometrics 0411002, EconWPA. [Downloadable!]
Other versions:
- Rossi, Barbara & Pesavento, Elena, 2003. "Do Technology Shocks Drive Hours Up or Down? A Little Evidence from an Agnostic Procedure," Working Papers 03-23, Duke University, Department of Economics. [Downloadable!]
- Elena Pesavento & Barbara Rossi, 2003. "Do Technology Shocks Drive Hours Up or Down? A Little Evidence From an Agnostic Procedure," Emory Economics 0326, Department of Economics, Emory University (Atlanta). [Downloadable!]
- Pesavento, Elena & Rossi, Barbara, 2005. "Do Technology Shocks Drive Hours Up Or Down? A Little Evidence From An Agnostic Procedure," Macroeconomic Dynamics, Cambridge University Press, vol. 9(04), pages 478-488, September. [Downloadable!]
Barbara Rossi & Elena Pesavento, 2004. "Do Technology Shocks Drive Hours Up or Down?," Econometric Society 2004 North American Summer Meetings 96, Econometric Society. [Downloadable!]
Elena Pesavento, 2005. "Residuals Bases Tests for the Null of No Cointegration: an Analytical Comparison," Emory Economics 0503, Department of Economics, Emory University (Atlanta). [Downloadable!]
Other versions:
- Elena Pesavento, 2007. "Residuals-based tests for the null of no-cointegration: an Analytical comparison," Journal of Time Series Analysis, Blackwell Publishing, vol. 28(1), pages 111-137, 01. [Downloadable!] (restricted)
Graham Elliott & Elena Pesavento, 2005. "Higher Power Tests for Bilateral Failure of PPP after 1973," Emory Economics 0502, Department of Economics, Emory University (Atlanta). [Downloadable!]

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