=SET NOECHO
PROC SEASROOT
* =====================================================================
* SHAZAM procedure for seasonal unit root testing for quarterly time series.
*
* References:
*  S. Hylleberg, R.F. Engle, C.W.J. Granger and B.S. Yoo, 1990,
*      "Seasonal Integration and Cointegration", Journal of Econometrics,
*      Vol. 44, pp. 215-238.
*  H.S. Lee and P.L. Siklos, 1991, "Unit Roots and Seasonal Unit Roots in
*      Macroeconomic Time Series", Economics Letters, Vol. 35, pp. 273-277.
*  G. Otto and T. Wirjanto, 1990, "Seasonal Unit Root Tests on Canadian
*      Macroeconomic Time Series", Economics Letters, Vol. 34, pp. 117-120.
*  
* Description:
*   With a quarterly time series X(t) consider the autoregression:
*   YD4(t)=P1*Y1(t)+P2*Y2(t)+P3*Y3(t)+P4*Y4(t) + e(t)
*   where:
*   YD4(t)=X(t)-X(t-4)
*   Y1(t)=X(t-1)+X(t-2)+X(t-3)+X(t-4)
*   Y2(t)=-[X(t-1)-X(t-2)+X(t-3)-X(t-4)]
*   Y3(t)=-[X(t-2)-X(t-4)]                 and
*   Y4(t)=X(t-1)-X(t-3)
*
*   Two augmented forms of the regression include:
*   (A) intercept, no seasonal dummies, no trend
*   (B) intercept, seasonal dummies, no trend
*
*   Test statistics to consider are:
*     1. t-test statistic for P1=0
*     2. t-test statistic for P2=0
*     3. F-test statistic for P3=0 and P4=0.
*
*   Critical values are tabulated in Hylleberg et al. (pp. 226-7).
*   5 % critical values (generated using 200 observations) are:
*             (A)      (B)
*     1.     -2.87    -2.91
*     2.     -1.92    -2.89
*     3.      3.12     6.61
*
*   If all tests are rejected then a series has no unit roots and
*   is stationary.
*   If test 2. and 3. are rejected then there are no seasonal unit roots.
*
* ===> Procedure Notes:
*  (1) Quarterly data is assumed.
*  (2) The data is transformed to logarithms. To suppress this change the
*      command MATRIX X_=LOG(X_) to MATRIX X_=X_.
*  (3) The regression can include additional lags of the regressand to
*      to whiten the errors. The commands below include D4X_(1.6) 
*      in the list of regressors. However, this is arbitrary and
*      the user may need to investigate the time series properties
*      further to decide on an appropriate lag choice.
*
*  Use:
*   FILE PROC SEASROOT
*   SAMPLE beg end
*   VARS: list of variables to individually test for unit roots.
*   EXEC SEASROOT
*
* Programmed by Diana Whistler, Revision Date: January 2002
*     E-mail: diana@shazam.econ.ubc.ca
* =====================================================================
SET NODOECHO NOOUTPUT
FORMAT(/' Seasonal unit root tests for variables:')
PRINT / FORMAT
PRINT VARS / NONAMES
FORMAT(/10X,'PI_  are tests with no seasonal dummies and'/ &
  10X,'PIQ_ are tests with seasonal dummies')
PRINT / FORMAT
FORMAT(/' Test statistics'/ &
  5X,'1.  test for a unit root at zero frequency'/ &
  5X,'2.  test for a bi-annual cycle root'/ &
  5x,'3.  test for an annual cycle root')
PRINT / FORMAT

COPY [VARS]  X_ / TROW=1,$N
* Take logs of the data
MATRIX X_=LOG(X_)
GEN1 N_=$COLS
GEN1 T_=$ROWS
DIM PI_ 3 PIQ_ 3
DO #=1,N_
* Generate regressors
SAMPLE 5 T_
SET NOWARN
GENR D4X_=X_:#-LAG(X_:#,4)
GENR S1_=  LAG(X_:#)+LAG(X_:#,2)+LAG(X_:#,3)+LAG(X_:#,4)
GENR S2_=-(LAG(X_:#)-LAG(X_:#,2)+LAG(X_:#,3)-LAG(X_:#,4))
GENR S3_=-(LAG(X_:#,2)-LAG(X_:#,4))
GENR S4_=  LAG(X_:#)-LAG(X_:#,3)
SET WARN
* Run a regression and get test statistics
OLS D4X_ S1_ S2_ S3_ S4_ D4X_(1.6) / TRATIO=TSTAT_
TEST
TEST S3_=0
TEST S4_=0
END
GEN1 PI_:3=$F
GEN1 PI_:1=TSTAT_:1
GEN1 PI_:2=TSTAT_:2
* Generate seasonal dummy variables
MATRIX QD_=SEAS(T_,4)
* Now include quarterly seasonal dummy variables in the regression.
OLS D4X_ S1_ S2_ S3_ S4_ D4X_(1.6) QD_ / NOCONSTANT TRATIO=TSTATQ_
TEST
TEST S3_=0
TEST S4_=0
END
GEN1 PIQ_:3=$F
GEN1 PIQ_:1=TSTATQ_:1
GEN1 PIQ_:2=TSTATQ_:2
* Print the results
FORMAT(/' Variable',F6.0)
PRINT $DO / FORMAT NONAMES
SAMPLE 1 3 
GENR TEST_=TIME(0)
FORMAT(5X,F5.0,2(5X,F10.4))
PRINT TEST_ PI_ PIQ_ / FORMAT
ENDO
DELETE / ALL_
SET DOECHO OUTPUT 
PROCEND
SET ECHO