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

Author

Listed:
  • Niels Haldrup

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

  • Michael Jansson

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

Abstract

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.

Suggested Citation

  • Niels Haldrup & Michael Jansson, 1999. "Spurious Regression, Cointegration, and Near Cointegration: A Unifying Approach," Tinbergen Institute Discussion Papers 99-005/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:19990005
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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.

    More about this item

    Keywords

    Cointegration; spurious regression; near cointegration; cointegration tests; local power function; brownian motion;
    All these keywords.

    JEL classification:

    • 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; Diffusion Processes

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