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Spurious Regression, Cointegration, and Near Cointegration: A Unifying Approach


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  • Niels Haldrup

    (Centre for Non-Linear Modelling in Economics, University of Aarhus)

  • Michael Jansson

    (Centre for Non-Linear Modelling in Economics, University of Aarhus)


This paper introduces a representation of an integrated vectortime series in which the coefficient of multiple correlation computed fromthe long-run covariance matrix of the innovation sequences is a primitiveparameter of the model. Based on this representation, a notion of nearcointegration is proposed and three separate applications of the model ofnear cointegration are provided. As a first application, we give analyticalcorroboration of the conjecture that the finite sample behavior ofF-statistics based on OLS estimators depends continuously on theaforementioned squared multiple correlation coefficient. Hence, the notionof near cointegration helps to bridge the gap between the polar cases ofspurious regression and cointegration. Secondly, we characterize theproperties of conventional cointegration methods under near cointegration,hereby investigating the robustness of cointegration methods. Finally, weillustrate how to obtain local power functions of cointegration tests thattake cointegration as the null hypothesis.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 99-005/4.

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Date of creation: 12 Feb 1999
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Handle: RePEc:dgr:uvatin:19990005

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Keywords: Cointegration; spurious regression; near cointegration; cointegration tests; local power function; brownian motion;

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  1. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, Econometric Society, vol. 56(5), pages 1021-43, September.
  2. Peter C.B. Phillips, 1987. "Weak Convergence of Sample Covariance Matrices to Stochastic Integrals via Martingale Approximations," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 846, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. Angela Huang, 2004. "Examining finite-sample problems in the application of cointegration tests for long-run bilateral exchange rates," Reserve Bank of New Zealand Discussion Paper Series DP 2004/08, Reserve Bank of New Zealand.


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