?===================================================================

? Iterative routine for multiplicative heteroskedasticity.         =

? Note that this replicates the HREG command.                      =

?                                                                  =

? User must define the data matrix with the following line:        =

?                                                                  =

?        NAMELIST         ; X = ... $                              =

?                                                                  =

? User's dependent variable is Y.  Change the following line       =

?                                                                  =

?        CREATE           ; Y = the dependent variable $           =

?===================================================================

? Heteroskedastic regression model:                                     

?                                                                       

? y  =  á'x  +  î,   Var[î]  =  exp(à'z)                                

?                                                                       

? (1) Starting values by least squares of Y on X for á, then the log    

?     of the squared residual on Z. Add 1.2704 to intercept to fix bias 

?                                                                       

  REGRESS  ;  lhs = Y ; rhs = X ; Res = e $                             

  MATRIX   ;  beta   = b $  (Retrieve estimate of á)                    

  CREATE   ;  logesq = log(e^2) $                                       

  REGRESS  ;  lhs = logesq ; rhs = Z $                                  

  MATRIX   ;  fix = 1.2704 / 0 ; alpha = b & fix $  (get estimate of à) 

?                                                                       

? (2) Iterative routine.  Based on á and à as they enter iteration      

?                                                                       

?     get e = (y - Xá), q = exp(à'z), and v = eý/q - 1                  

?     New á is weighted LS with weights 1/q,                            

?     New à is old à + slopes in regression of v on Z.                  

?     Exit if this update to à is small. c(1) = maximum change in à.    

?                                                                       

  PROC

    CREATE ; e = y - dot(X,beta) 

           ; q1=exp(-dot(Z,alpha)) ; v=e^2*q1 - 1 $ 

    REGRESS; lhs = v ; rhs = Z $                                          

    MATRIX ; alpha = alpha & b ; c(1) = chng(b) $                         

    REGRESS; lhs = y ; Rhs = X ; Wts = q1 $

  ENDPROC

  EXEC   ; query $