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)