/*
  THIS IS THE SECOND OF FOUR SAS PROGRAMS TO BE USED TO COMPLETE YOUR 
"SUPER" PROBLEM.  THIS PROGRAM ALLOWS YOU TO DETERMINE THE BEST TRANSFER
FUNCTION MODEL FOR RELATING YOUR X?? SERIES (THE LEADING INDICATOR) WITH 
YOUR Y?? SERIES (THE TARGET VARIABLE). */

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

  ; 

/*  THE NEXT PROC ARIMA STATEMENT ALLOWS YOU TO CONSTRUCT THE CROSS-
    CORRELATIONS FUNCTION.  IN THE STATEMENTS IMMEDIATELY BELOW YOU
    HAVE TO REPLACE THE QUESTIONS MARKS FOR P AND Q THAT BEST DESCRIBE 
    THE BOX-JENKINS MODEL FOR YOUR LEADING INDICATOR X.  */
 
PROC ARIMA DATA=ONE(OBS=80);
  IDENTIFY VAR = X NOPRINT;
  ESTIMATE P=? Q=? METHOD=CLS MAXIT=50;
  IDENTIFY VAR = Y CROSSCOR = (X) NLAG = 12;

/*
  ONCE YOU HAVE MADE YOUR TENTATIVE IDENTICATION OF YOUR TRANSFER
  FUNCTION MODEL, YOU NEED TO DETERMINE IF YOUR TENTATIVE CHOICE 
  SHOULD BE MADE YOUR FINAL CHOICE.  YOU DO SO BY OVERFITTING YOUR 
  TENTATIVE CHOICE.  TO DO THIS YOU NEED TO ADD SOME ESTIMATE STATEMENTS
  TO YOUR PROGRAM.  REMEMBER THAT YOU MIGHT HAVE TO "SOP UP" SOME REMAINING
  AUTOCORRELATION IN THE RESIDUALS OF YOUR "BETTER" MODEL BY INSERTING 
  P=? AND Q=? BETWEEN THE "ESTIMATE" AND "INPUT" PARTS OF THE TRANSFER 
  FUNCTION ESTIMATE STATEMENTS.

  BELOW ARE SOME "EXAMPLE" TRANSFER FUNCTION ESTIMATE STATEMENTS.
  THE MODELS EXAMINED BELOW ARE (IN ORDER): B=1,R=0,S=0/
  B=1,R=1,S=0/ B=1,R=0,S=1/ AND B=1,R=1,S=1.  NOTE THAT IN THE
  LAST MODEL WE "SOP UP" THE RESIDUAL AUTOCORRELATION IN THE
  IN THE ERRORS BY TRYING P=1 AND Q=0, AN AR(1) MODEL FOR
  THE RESIDUALS. ALSO NOTE THAT THESE EXAMPLE INPUT STATEMENTS
  MAY NOT BE APPROPRIATE FOR YOUR PARTICULAR SERIES BUT YOU CAN
  ADAPT THEM TO YOUR OWN TENTATIVE VALUES OF B, R, AND S.

  ESTIMATE INPUT = (1$X) METHOD=ML MAXIT=50;
  ESTIMATE INPUT = (1$(1)X) METHOD=ML MAXIT=50;
  ESTIMATE INPUT = (1$/(1)X) METHOD=ML MAXIT=50;
  ESTIMATE P=1 Q=0 INPUT = (1$(1)/(1)X) METHOD=ML MAXIT=50;
*/

/*  PUT YOUR ESTIMATE STATEMENTS IN THE SPACE FOLLOWING THIS
    COMMENT.  */




/* DON'T FORGET TO OVERFIT THE MODEL YOU TENTATIVELY CHOOSE FROM THE 
   CROSS-CORRELATION FUNCTION.  ARE ALL OF THE COEFFICIENTS OF YOUR
   FINAL MODEL STATISTICALLY SIGNIFICANT (APART FROM MU)?  ARE THE 
   RESIDUALS OF YOUR FINAL MODEL WHITE NOISE?  DO THE OVERFITTING 
   EXERCISES SUPPORT YOUR FINAL MODEL CHOICE?  */  
  
/* THIS COMPLETES THE PROGRAM SPRO2.SAS  */