PROC JOHANSEN
* ========================================================================
*             Johansen Tests for Cointegration 
*
* Reference: S. Johansen and K. Juselius, "Maximum Likelihood Estimation
*     and Inference on Cointegration - with Applications to the Demand
*     for Money", OXFORD BULLETIN OF ECONOMICS AND STATISTICS, Vol 52,
*     1990, pp. 169-210.
*
* Equation numbers refer to the above paper.
*
* Notes:
* (1) The model includes a constant term and three seasonal dummies.
*     This is appropriate for quarterly time series.
* (2) No restrictions on the constant term are imposed. This allows
*     for linear trends in the data. 
*
* Critical values for the test statistics are tabulated in
* Johansen and Juselius (1990), Table A2.
*
* TRACE TEST
* Null hypothesis: No. of cointegrating vectors is less than or equal to r.
*
*          10 % critical values             5 % critical values
*   r    p=2    p=3     p=4    p=5    r    p=2    p=3     p=4    p=5
*   -------------------------------   -------------------------------
*   4                          6.7    4                          8.1
*   3                   6.7   15.6    3                   8.1   17.8
*   2            6.7   15.6   28.4    2            8.1   17.8   31.3
*   1     6.7   15.6   28.4   45.2    1     8.1   17.8   31.3   48.4
*   0    15.6   28.4   45.2   66.0    0    17.8   31.3   48.4   70.0
*     r = number of cointegrating vectors
*     p = number of time series
*
* MAXIMUM EIGENVALUE TEST
* Null hypothesis: No. of cointegrating vectors is r.
* Alternative: r+1 cointegrating vectors
*
*          10 % critical values             5 % critical values
*   r    p=2    p=3     p=4    p=5    r    p=2    p=3     p=4    p=5
*   -------------------------------   -------------------------------
*   4                          6.7    4                          8.1
*   3                   6.7   12.8    3                   8.1   14.6
*   2            6.7   12.8   19.0    2            8.1   14.6   21.3
*   1     6.7   12.8   19.0   24.9    1     8.1   14.6   21.3   27.3
*   0    12.8   19.0   24.9   30.8    0    14.6   21.3   27.3   33.3
*
* ===> WARNINGS
* (1) The data is transformed to logarithms. If this is not desired then
* change the command MATRIX X_=LOG(X_) to MATRIX X_=X_
* (2) If quarterly seasonal dummies are not required then change the 
* command MATRIX QD_=SEAS(T_,4) to GENR QD_=1
*
*  Use:
*   FILE PROC JOHANSEN
*   SAMPLE beg end
*   NLAG: lag k  (k > 1)
*   VARS: list of time series
*   EXEC JOHANSEN
*  
* Programmed by Diana Whistler, Revision: April, 2000
*     E-mail: diana@shazam.econ.ubc.ca
* ========================================================================
SET NOECHO
SET NODOECHO
SET NOOUTPUT
COPY [VARS] X_ / TROW=1,$N
* Take logs of the data
MATRIX X_=LOG(X_)
GEN1 P_=$COLS
GEN1 T_=$ROWS
* Generate seasonal dummy variables
MATRIX QD_=SEAS(T_,4)
*GENR QD_=1
SAMPLE 2 T_
* Generate first differences
MATRIX DX_=X_-LAG(X_)
* Allocate arrays to store results
GEN1 NLAG_=[NLAG]
IF1(NLAG_.LT.2) NLAG_=2
PRINT NLAG_
GEN1 NLL_=NLAG_-1
GEN1 KK_=P_*NLL_
DIM  EA0_ T_ P_ EAK_ T_ P_  DXVEC_ T_ KK_
GEN1 BEG_=NLAG_ + 1
SAMPLE BEG_ T_
DO #=1,P_
* Generate NLAG-period lagged variables
GENR LY#_=LAG(X_:#,NLAG_)
ENDO
* Set up a matrix of lagged variables to use as regressors
GEN1 C1_=1
DO #=1,NLL_
GEN1 C2_=C1_+P_-1
GEN1 R1_=#+1
GEN1 R2_=T_-#
COPY DX_ DXVEC_ / FROW=1;R2_ TROW=R1_;T_ FCOL=1;P_ TCOL=C1_;C2_  
GEN1 C1_=C2_+1
ENDO
* Obtain the residuals stated in Equation (3.6) and (3.7)
DO #=1,P_
* Regress first differences on the lagged differences 
OLS DX_:# DXVEC_ QD_ / RESID=EA0_:# NOCONSTANT
* Regress NLAG-period lags on the lagged differences 
OLS LY#_  DXVEC_ QD_ / RESID=EAK_:# NOCONSTANT
ENDO
GEN1 T1_=$N
COPY EA0_ E0_ / FROW=BEG_;T_ TROW=1;T1_ FCOL=1;P_ TCOL=1;P_
COPY EAK_ EK_ / FROW=BEG_;T_ TROW=1;T1_ FCOL=1;P_ TCOL=1;P_
* Note: the MATRIX command ignores the current SAMPLE command
* Do the calculations in Equation (3.9)
MATRIX S00_=E0_'E0_/T1_
MATRIX S0K_=E0_'EK_/T1_
MATRIX SKK_=EK_'EK_/T1_
* Cholesky decomposition - SKK=CC'
MATRIX C_=CHOL(SKK_)
MATRIX CINV_=INV(C_)
* Matrix B is a symmetric positive definite matrix
MATRIX B_=CINV_*S0K_'INV(S00_)*S0K_*CINV_'
* Get the eigenvalues of B (real and positive) in descending order
MATRIX LAMBDA_=EIGVAL(B_)
SAMPLE 1 P_
SORT LAMBDA_ 
GENR LMAX_=-T1_*LOG(1-LAMBDA_)
* Construct likelihood ratio test statistics from Equation (4.8)
GENR LTRACE_=-T1_*SUM(LOG(1-LAMBDA_))
GENR R_=P_-TIME(0)
** The variables analyzed are:
PRINT VARS / NONAMES
FORMAT(5X,F5.0,8X,F10.3,3X,F10.3)
PRINT R_ LTRACE_ LMAX_ / FORMAT
DELETE / ALL_
SET DOECHO
SET OUTPUT
SET ECHO
PROCEND