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Zbl 0613.62140
Engle, Robert F.; Granger, C.W.J.
Co-integration and error correction: Representation, estimation, and testing. (English)
[J] Econometrica 55, 251-276 (1987). ISSN 0012-9682; ISSN 1468-0262/e

The paper explores the relationship between co-integration and error correction models and develops estimation procedures and tests for co- integration. The components of the vector $x\sb t$ are co-integrated of order b,d, if all components of $x\sb t$ are integrated of order d and there exists a vector $\alpha$ ($\ne 0)$ such that $z\sb t=\alpha 'x\sb t$ is integrated of order d-b, $b>0$. The vector $\alpha$ is called the co-integrating vector. Special emphasis is given to the case in which $\alpha 'x\sb t=0$. This situation has the immediate interpretation of a long-run equilibrium so that co-integration implies that deviations from equilibrium are stationary with finite variance despite of the fact that the series themselves are nonstationary and have infinite variances. \par By use of the second author's representation theorem [Co-integrated variables and error-correcting models. UCSD discussion paper 83-13 (1983)] the authors show how co-integrated systems are connected by moving average, autoregressive, and error correction representations. Furthermore, the authors present an asymptotically efficient two-step estimator. Testing for co-integration combines the problems of testing for unit roots and tests with parameters which are not identified under the null. Several test statistics are suggested and the critical values for these statistics obtained by a Monte Carlo simulation are given. The paper closes with some applications.
[H.S.Buscher]

MSC 2000:: *62P20 Appl. of statistics to economics
62M10 Time series, etc. (statistics)
91B84 Economic time series analysis

Keywords: multivariate time series; Dickey-Fuller tests; co-integration; error correction models; estimation; long-run equilibrium; representation theorem; testing for unit roots; critical values

Cited in: Zbl 1178.62098 Zbl 1053.91086 Zbl 0967.62063 Zbl 0968.62064 Zbl 0948.91056 Zbl 0885.62107 Zbl 0834.62083 Zbl 0782.62102 Zbl 0761.62164 Zbl 0751.62052 Zbl 0733.62100 Zbl 0693.90031 Zbl 0649.62108

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