Johansen, Søren Statistical analysis of cointegration vectors. (English) Zbl 0647.62102 J. Econ. Dyn. Control 12, No. 2-3, 231-254 (1988). Summary: 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. Cited in 16 ReviewsCited in 493 Documents 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 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Ahn, S. K.; Reinsel, G. C., Estimation for partially nonstationary multivariate autoregressive models (1987), University of Wisconsin: University of Wisconsin Madison, WI [2] Anderson, T. W., An introduction to multivariate statistical analysis (1984), Wiley: Wiley New York · Zbl 0651.62041 [3] Andersson, S. A.; Brøns, H. K.; Jensen, S. 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