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:
Ŷt = - 0,407 + 1,983 √ht
(t) (-2,862) (5,243)
Ht = 0,022 + (0,211 – 0,211dt-1)e²t-1 + 0,782 ht-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 - muscalar T =
$nobsloop 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 loopseries h = lhreturn series leend functionopen
c:\Temp\ukscalar mu = 0.8scalar gam = 0.1scalar alpha = 0.4scalar beta = 0scalar delta =
0.5scalar theta = 0.1series h = NAmle 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 betaend mle --robust Would you be so kind to look after this exercise and let me know
something?Yours faithfully, Maarten
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