Spurious Regression, Cointegration, and Near Cointegration: A Unifying Approach
AbstractThis 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 InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 99-005/4.
Date of creation: 12 Feb 1999
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Web page: http://www.tinbergen.nl
Cointegration; spurious regression; near cointegration; cointegration tests; local power function; brownian motion;
Other versions of this item:
- Jansson, Michael & Haldrup, Niels Prof., 2000. "Spurious Regression, Cointegration, and Near Cointegration: A Unifying Approach," University of California at San Diego, Economics Working Paper Series qt5b13w0rp, Department of Economics, UC San Diego.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-1999-05-03 (All new papers)
- NEP-ECM-1999-05-03 (Econometrics)
- NEP-ETS-1999-05-03 (Econometric Time Series)
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.:
- Peter C.B. Phillips, 1987.
"Weak Convergence of Sample Covariance Matrices to Stochastic Integrals via Martingale Approximations,"
Cowles Foundation Discussion Papers
846, Cowles Foundation for Research in Economics, Yale University.
- Phillips, P.C.B., 1988. "Weak Convergence of Sample Covariance Matrices to Stochastic Integrals Via Martingale Approximations," Econometric Theory, Cambridge University Press, vol. 4(03), pages 528-533, December.
- 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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