Dear sir or madam,

I'm a belgian student and this week I've been studying my course of Advanced Business Econometrics. I'm using the book ' Principles of Econometrics' (3rd version) from Hill, Griffiths & Lim. Now I am at Chapter 14: Time varying volatility and ARCH models. I got a problem with ex. 14.10 p. 381: this GARCH in mean model is written as a function of the time-varying standard deviation. The main problem is: I don't know how to write the time-varying standard deviation in the right form in the script. At the moment, my script seems like this (I thing the red piece is missing, but that's not enough I think):

Estimate a T-GARCH-in-mean model and check that you obtain the following results:

Ŷ_t = - 0,407 + 1,983 √h_t

(t) (-2,862) (5,243)

H_t = 0,022 + (0,211 – 0,211d_t-1)e²_t-1 + 0,782 h_t-1

(4,697) (8,952) (-8,728) (27,677)

my script seems like this:

function gim_filter(series y, \
scalar mu, scalar theta, scalar delta, scalar alpha, \
scalar gam, scalar beta, series *h)
series lh = var(y)
series le = y - mu
scalar T = $nobs
loop for i=3..T --quiet
    scalar ilag = $i - 1
    scalar d = (le[ilag]<0)
    scalar e2lag = le[ilag]^2
    lh[i] = delta + alpha*e2lag + gam*e2lag*d + beta*lh[ilag]
    le[i] = le[i] - theta*lh[i]^(1/2)
end loop
series h = lh
return series le
end function
open c:\Temp\uk
scalar mu = 0.8
scalar gam = 0.1
scalar alpha = 0.4
scalar beta = 0
scalar delta = 0.5
scalar theta = 0.1
series h = NA
mle ll = -0.5*(log(2*pi) + log(h) +(e^2)/h)
    e = gim_filter(r, mu, theta, delta, alpha, gam, beta, &h)
    params mu theta delta alpha gam beta
end mle --robust

Would you be so kind to look after this exercise and let me know something?

Yours faithfully,

Maarten

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