Name

garch_grad — Generates garch gradient

CALLING SEQUENCE

[g,dht,gradt]=garch_grad(parm,nar,nma,y,x)

PARAMETERS

Input

• parm= vector of parameters (beta, a0, ar and ma in that order)

• nar = # of ar parameters

• nma = # of ma parameters

• y = (n x 1) vector of the endogenous variable

• x = (n x k) vector of the exogenous variables

Output

• g = (k+nar+nma+1 x 1) -gradient at param

• dht = (nobs x nar+nma+1) derivative of sigt w.r.t a0, ar, ma

• scores = (k+nar+nma+1 x 1) sub-gradient at each date

DESCRIPTION

Generates garch likelihood gradient with respect to the true garch parameters. This in not the function used for maximisation, because maximised parameters are transformed in order to insure the positivity of the variance.

EXAMPLE

[g,dht,scores]=garch_grad(parmd,nar,nma,grocer_y,grocer_x)
 
Example taken from function garch().  

               

AUTHOR

Eric Dubois 2002