Statistical analysis of cointegration vectors.

*(English)*Zbl 0647.62102Summary: We consider a nonstationary vector autoregressive process which is integrated of order 1, and generated by i.i.d. Gaussian errors. We then derive the maximum likelihood estimator of the space of cointegration vectors and the likelihood ratio test of the hypothesis that it has a given number of dimensions. Further we test linear hypotheses about the cointegration vectors.

The asymptotic distribution of these test statistics are found and the first is described by a natural multivariate version of the usual test for unit root in an autoregressive process, and the other is a \(\chi^2\) test.

The asymptotic distribution of these test statistics are found and the first is described by a natural multivariate version of the usual test for unit root in an autoregressive process, and the other is a \(\chi^2\) test.

##### MSC:

62P20 | Applications of statistics to economics |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62E20 | Asymptotic distribution theory in statistics |

62H15 | Hypothesis testing in multivariate analysis |

##### Keywords:

chi-square test; nonstationary vector autoregressive process; Gaussian errors; maximum likelihood estimator; cointegration vectors; likelihood ratio test; linear hypotheses
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\textit{S. Johansen}, J. Econ. Dyn. Control 12, No. 2--3, 231--254 (1988; Zbl 0647.62102)

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