/*  THIS IS THE FIRST OF FOUR SAS PROGRAMS THAT YOU NEED TO RUN TO 
COMPLETE YOUR "SUPER" PROBLEM.  FIRST, THIS PROGRAM PLOTS YOUR X?? AND Y??
SERIES AND CALCULATES THEIR AUTOCORRELATION FUNCTIONS.  YOU ARE TO 
ASSUME THAT BOTH SERIES ARE STATIONARY SINCE THEIR AUTOCORRELATION 
FUNCTIONS DAMP OUT REASONABLY QUICKLY.  WE USE ONLY THE ESTIMATION DATA 
SET (OBS. 1 - 80).  SECOND, THE PROGRAM HELPS YOU DETERMINE THE 
APPROPRIATE BOX-JENKINS MODEL FOR YOUR LEADING INDICATOR X??.  YOU NEED 
TO KNOW THE BOX-JENKINS MODEL FOR X?? BEFORE YOU CAN CALCULATE THE 
CROSS-CORRELATION FUNCTION BETWEEN X?? AND YOUR TARGET VARIABLE Y??. */

/* You should cut and paste the data you have been given in the
   empty space below under the "cards" statement.  Then you should
   replace the question marks with the number of the series you have
   been assigned in class. */

 DATA ONE;
 input obs x?? y??;
  x = x??;
  y = y??;
  cards;

  ;
  
/*  THIS SEGMENT OF THE PROGRAM PRINTS THE X AND Y SERIES YOU ARE WORKING 
WITH.  NOTE:  THE FIRST 80 OBSERVATIONS CONSTITUTES THE ESTIMATION DATA 
SET AND THE LAST 30 OBSERVATIONS CONSTITUTES THE HOLD-OUT SAMPLE DATA SET.  */
 
PROC PRINT DATA=ONE(OBS=80);
  VAR X Y;
  TITLE 'ESTIMATION DATA SET: OBS. 1 - 80';

PROC PRINT DATA=ONE(FIRSTOBS=80);
  VAR X Y;
  TITLE 'HOLD-OUT DATA SET: OBS. 81 - 110';

/* THIS SEGMENT OF THE PROGRAM PLOTS THE ESTIMATION DATA SETS FOR X AND
   Y.  DO THE SERIES LOOK STATIONARY? */ 

DATA ONE;
  SET ONE;
  OBS=_N_;

PROC PLOT DATA=ONE(OBS=80);
  PLOT X*OBS;
  TITLE 'PLOT OF ESTIMATION DATA SET FOR X';

PROC PLOT DATA=ONE(OBS=80);
  PLOT Y*OBS;
  TITLE 'PLOT OF ESTIMATION DATA SET FOR Y';

PROC PRINT DATA=_NULL_;
  TITLE ' ';

/* THIS SEGMENT OF THE PROGRAM PLOTS THE AUTOCORRELATION FUNCTIONS
   FOR THE ESTIMATION DATA ON YOUR X AND Y SERIES.  ARE THEY 
   SLOWLY OR QUICKLY DAMPING?  */ 

PROC ARIMA DATA=ONE(OBS=80);
  IDENTIFY VAR = X;

PROC ARIMA DATA=ONE(OBS=80);
  IDENTIFY VAR = Y; 

/* LOOK AT THE ACF FOR THE X SERIES AND MAKE A PRELIMINARY IDENT-
IFICATION OF P AND Q.  */
 
/* NOW LET'S OBTAIN THE INGREDIENTS FOR A P-Q BOX FOR YOUR X SERIES. */

PROC ARIMA DATA=ONE(OBS=80);
  IDENTIFY VAR=X NOPRINT;
  ESTIMATE P=0 Q=0 METHOD = ML MAXIT = 50;
  ESTIMATE P=0 Q=1 METHOD = ML MAXIT = 50;
  ESTIMATE P=0 Q=2 METHOD = ML MAXIT = 50;
  ESTIMATE P=0 Q=3 METHOD = ML MAXIT = 50;
  ESTIMATE P=1 Q=0 METHOD = ML MAXIT = 50;
  ESTIMATE P=2 Q=0 METHOD = ML MAXIT = 50;
  ESTIMATE P=1 Q=1 METHOD = ML MAXIT = 50;

  run;

/*
  AT THIS STAGE YOU SHOULD HAVE A TENTATIVE MODEL FOR THE BOX-JENKINS
  MODEL FOR YOUR X SERIES.  NOW YOU NEED TO CONDUCT AN OVERFITTING
  EXERCISE ON TENTATIVE MODEL CHOSEN FROM THE P-Q BOX.  SUPPOSE THAT 
  FROM THE P-Q BOX YOUR TENTATIVE MODEL IS AR(1), I.E. P=1 AND Q=0.
  THEN LOOK AT THE T-STATISTICS OF THE INCREMENTAL COEFFICIENTS FOR THE 
  AR(2) AND ARMA(1,1) MODELS.  NOTE: THE ABOVE MODELS MAY NOT INCLUDE 
  ALL OF THE OVERFITTING MODELS YOU NEED.  IN THIS CASE YOU WILL HAVE 
  TO ADD SOME ESTIMATE STATEMENTS TO YOUR PROGRAM.  YOU SHOULD NOW HAVE 
  SETTLED ON YOUR FINAL CHOICE OF BOX-JENKINS MODEL FOR YOUR X SERIES.    
*/

/* THIS COMPLETES THE SAS PROGRAM SPRO1.SAS  */