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

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Author Info
Niels Haldrup () (Centre for Non-Linear Modelling in Economics, University of Aarhus)
Michael Jansson (Centre for Non-Linear Modelling in Economics, University of Aarhus)

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Abstract

This paper introduces a representation of an integrated vector time series in which the coefficient of multiple correlation computed from the long-run covariance matrix of the innovation sequences is a primitive parameter of the model. Based on this representation, a notion of near cointegration is proposed and three separate applications of the model of near cointegration are provided. As a first application, we give analytical corroboration of the conjecture that the finite sample behavior of F-statistics based on OLS estimators depends continuously on the aforementioned squared multiple correlation coefficient. Hence, the notion of near cointegration helps to bridge the gap between the polar cases of spurious regression and cointegration. Secondly, we characterize the properties of conventional cointegration methods under near cointegration, hereby investigating the robustness of cointegration methods. Finally, we illustrate how to obtain local power functions of cointegration tests that take cointegration as the null hypothesis.

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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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Web page: http://www.tinbergen.nl/

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

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models

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  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. [Downloadable!]
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