Maximum likelihood estimates of cointegration [STB-21: sts9] ---------------------------------------------^mlcoint^ varlist [^if^ exp] [^in^ range] [^, noc^onstant ^l^ags^(^#^)^ ^non^ormal ^r^egress ^stand^ard ^s^tatic^(^varlist^)^ ]

^lrcotest^ varlist [^,^ ^c^ir^(^#^)^ ^r^estrict ]

^wcotest^ varlist [^,^ ^c^ir^(^#^)^ ]

^mlcoint^ calculates the eigenvalues and the maximal eigenvalue and trace statistics for the VAR defined by ^varlist^. These statistics can be used to test for the number of cointegrating vectors in the system. If the ^normal^ or ^standard^ option is specified, maximum likelihood estimates of the cointegrating vectors and of the matrix of weights are displayed. ^mlcoint^ uses Johansen's method for computing the estimates and test statistics. See the references for more information on the method.

^lrcotest^ and ^wcotest^ are used after ^mlcoint^ to test the null hypothesis that one or more of the variables in the VAR do not enter the cointegrating relationship(s). ^lrcotest^ calculates the likelihood-ratio test. ^wcotest^ calculates the Wald test.

Notes ----- These programs rely on programs in the Stata time series library (STB-21: sts7.4). The time series library must be available before ^mlcoint^ , ^lrcotes > t^, or ^wcotest^ can be run.

^mlcoint^ creates several global matrices that are used by ^lrcotest^ and ^wcot > est^. These matrices have names that begin with the characters "^M_^".

Options ------- ^c^ir^(^#^)^ indicates the number of cointegrating relationships in the system.

^noconstant^ suppresses the constant in the first stage VAR.

^l^ags^(^#^)^ specifies the number of lags in the original VAR (in levels).

^non^ormal suppresses the display of the normalized Alpha and Beta' matrices.

^r^egress indicates that the VAR estimates are to be displayed.

^r^estrict requests that ^lrcotest^ display the restricted estimates of the eigenvalues and of the Alpha and Beta' matrices.

^stand^ard requests the display of the standardized Alpha and Beta' matrices instead of the normalized matrices.

^s^tatic^(^varlist^)^ specifies static variables that enter the VAR.

References ----------

Johansen, S. 1988. "Statistical Analysis of Cointegration Vectors," ^Journal of Economic Dynamics and Control^. Vol. 12 pp. 231-254.

Johansen, S. and Katarina Juselius. 1990. "Maximum Likelihood Estimation and Inference on Cointegration - With Applications to the Demand for Money," ^Oxford Bulletin of Economics and Statistics^. Vol. 52 pp. 169-210.

Authors -------

Ken Heinecke and Charles Morris Federal Reserve Bank of Kansas City FAX 816-881-2199

Also see --------

STB: sts9 (STB-21), sts7.4 (STB-21)