?  Estimator for a Geometric Lag Model

?  Assumes dependent variable is Y and one independent variable, 

?  named X.

?  First define matrices to keep parameters and sums of squares

?

             MATRIX ; EE = INIT(19,1,0) ; L = INIT(19,1,0) $

?

?  Set up initial value of the subscript and estimation criterion

? 

             CALC   ;  i  =  1  ;  eemin  = 9999999 ;  best = 0 $

?

?  Now define the procedure to estimate the regression and keep the results.  We also retain the 

?  optimal value of lambda by using two indirect CALC commands in MATRIX.

?

             PROCEDURE

                    SAMPLE       ; 1 $ 

                    CREATE       ; z  =  lambda  ; xstar = x $

                    SAMPLE       ; 2 - ... the end of the sample $

                    CREATE       ; z=lambda*z[-1] ; xstar=x+lambda*xstar[-1] $

                    SAMPLE       ; 1 - ... the end of the sample $

                    REGRESS      ; Lhs = y ; Rhs = One,z,xstar $

                    MATRIX       ; EE(i) = sumsqdev ; L(i) = lambda

                                 ; if [ sumsqdev < eemin] best = lambda

                                 ; eemin = sumsqdev $

                    CALC         ; i = i + 1 $

             ENDPROC

?

?   Execute the procedure

?

             EXECUTE             ; lambda = .05, .95, .05 $

             MPLOT               ; Lhs=L ; Rhs=EE ; Fill ; endpoints=0,1 $

             SAMPLE       ; 1  $ 

             CREATE       ; delta  =  0  $

             SAMPLE       ; 2  $ 

             CREATE       ; delta  =  x  $

             SAMPLE       ; 3  -  ... end of sample $ 

             CREATE       ; delta  =  xstar[-1] + lambda * delta[-1] $

             SAMPLE       ; 1  -  ... end of sample $ 

             CREATE       ; t=trn(1,1)

                          ; d=b(2)*delta + t * b(3) * lambda^(t-1) $



To get the covariance matrix, the one matrix command,



             MATRIX       ; Var = ssqrd * XPXI (one,xstar,z,d) $



is sufficient.  The statistical results could be displayed with



             MATRIX       ; est = b / lambda ; STAT (est,var) $  of sample $ 

             CREATE       ; delta  =  xstar[-1] + lambda * delta[-1] $

             SAMPLE       ; 1  -  ... end of sample $ 

             CREATE       ; t=trn(1,1)

                          ; d=b(2)*delta + t * b(3) * lambda^(t-1) $



To get the covariance matrix, the one matrix command,



             MATRIX       ; Var = ssqrd * XPXI (one,xstar,z,d) $



is sufficient.  The statistical results could be displayed with



             MATRIX       ; Stat (EST,VAR) $