Hi Chris, To the best of my knowledge Hamilton in „Time Series Analysis“, Chapter 21 talks about the relationship between GARCH and ARMA. Hope that helps. Best regards Joerg _____ From: gretl-users-bounces(a)lists.wfu.edu [mailto:gretl-users-bounces@lists.wfu.edu] On Behalf Of Chris Sent: Tuesday, 5. June 2007 5:56 PM To: Gretl list Subject: [Gretl-users] arima + arch ? is there any way to combine arima with arch? Is this a stupid question? When I run the arima stuff I get a fantastic fit to the data, but when I run the arch test it shows I definitely have an arch process. Thanks, Chris

Hi, Your script is confusing me a bit;) so if I had an arch process that was arch 24 and arima 1 1 would I change the script to this: open "C:\Documents and Settings\cquilley\Application Data\gretl\mydata.gdt" /* compute 1-step pred. errs + cond. variances */ function filter(series y, \ scalar arpar, scalar mapar, \ scalar om, scalar alpha1, scalar alpha2, \ scalar alpha3, scalar alpha4, scalar alpha5, \ scalar alpha6, scalar alpha7, scalar alpha8, \ scalar alpha9, scalar alpha10, scalar alpha11, \ scalar alpha12, scalar alpha13, scalar alpha14, \ scalar alpha15, scalar alpha16, scalar alpha17, \ scalar alpha18, scalar alpha19, scalar alpha20, \ scalar alpha21, scalar alpha22, scalar alpha23, \ scalar alpha24, \ series *e, series *h) scalar err = 0 scalar T = $nobs series e = 0 series h = om/(1-alpha1-alpha2-alpha3-alpha4-alpha5-alpha6-alpha7-alpha8-alpha9-alpha10-alpha11-alpha12-alpha13-alpha14-alpha15-alpha16-alpha17-alpha18-alpha19-alpha20-alpha21-alpha22-alpha23-alpha24) loop for i=2..T --quiet scalar e2lag = e[i-1]^2 scalar e3lag = e[i-2]^2 scalar e4lag = e[i-3]^2 scalar e5lag = e[i-4]^2 scalar e6lag = e[i-5]^2 scalar e7lag = e[i-6]^2 scalar e8lag = e[i-7]^2 scalar e9lag = e[i-8]^2 scalar e10lag = e[i-9]^2 scalar e11lag = e[i-10]^2 scalar e12lag = e[i-11]^2 scalar e13lag = e[i-12]^2 scalar e14lag = e[i-13]^2 scalar e15lag = e[i-14]^2 scalar e16lag = e[i-15]^2 scalar e17lag = e[i-16]^2 scalar e18lag = e[i-17]^2 scalar e19lag = e[i-18]^2 scalar e20lag = e[i-19]^2 scalar e21lag = e[i-20]^2 scalar e22lag = e[i-21]^2 scalar e23lag = e[i-22]^2 scalar e24lag = e[i-23]^2 scalar e25lag = e[i-24]^2 e[i] = y[i] - (arpar*y[i-1] + mapar*e[i-1]) h[i] = om + alpha1*e2lag + alpha2*e3lag + alpha3*e4lag \ + alpha4*e5lag + alpha5*e6lag + alpha6*e7lag + alpha7*e8lag \ + alpha8*e9lag + alpha9*e10lag + alpha10*e11lag + \ alpha11*e12lag + alpha12*e13lag + alpha13*e14lag + \ alpha14*e15lag + alpha15*e16lag + alpha16*e17lag + \ alpha17*e18lag +alpha18*e19lag + alpha19*e20lag + \ alpha20*e21lag + alpha21*e22lag +alpha22*e23lag + \ alpha23*e24lag + alpha24*e25lag end loop return scalar err end function /* now with a non-zero an MA part */ series y = TOTAL scalar phi = 0 scalar theta = 0 scalar a1 = 0.1 scalar a2 = 0.1 scalar a3 = 0.1 scalar a4 = 0.1 scalar a5 = 0.1 scalar a6 = 0.1 scalar a7 = 0.1 scalar a8 = 0.1 scalar a9 = 0.1 scalar a10 = 0.1 scalar a11 = 0.1 scalar a12 = 0.1 scalar a13 = 0.1 scalar a14 = 0.1 scalar a15 = 0.1 scalar a16 = 0.1 scalar a17 = 0.1 scalar a18 = 0.1 scalar a19 = 0.1 scalar a20 = 0.1 scalar a21 = 0.1 scalar a22 = 0.1 scalar a23 = 0.1 scalar a24 = 0.1 scalar omega = var(y)*(1-a1-a2-a3-a4-a5-a6-a7-a8-a9-a10-a11-a12-a13-a14-a15-a16-a17-a18-a19-a20-a21-a22-a23-a24) series ht = 1 series et = 0 mle loglik = -0.5*(log(ht) + ut) scalar err = filter(y, phi, theta, omega, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a15, a15, a16, a17, a18, a19, a20, a21, a22, a23, a24, &et, &ht) series ut = et^2/ht params phi, theta, omega, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a15, a15, a16, a17, a18, a19, a20, a21, a22, a23, a24 end mle --verbose ? When I run this I get the error "Bad character 'i' in date string" and the script halts. Also, the script only appears to output the estimated alphas and arima coefficients. How would I modify this to get a more garch like output with coefficients estimated for the function total = B1 + B2*X2 + B3*X3? i.e how do I get it to estimate the B's as well? Thanks, Chris On 6/5/07, Riccardo (Jack) Lucchetti <r.lucchetti(a)univpm.it&gt; wrote:

Hi, The actual model isn't just based on the Y variable, it's of the form y = B1 + B2*X2 + B3*X3 . in your example you seem to generate only a Y variable and doing everything with the Y variable. I think the major problem here is I may not be understanding what I'm doing;) in gretl, when you run an arima model it estimates a bunch of stuff (the arima process) and then estimates the betas on your other explanatory variables. The same happens when you estimate a garch process. The output for the script only generates estimates of the arma process variables and the garch process variables. I'm trying to figure out how to estimate the coefficients on the other explanatory variables as well... I really appreciate your help, Sincerely, Chris On 6/7/07, Riccardo (Jack) Lucchetti <r.lucchetti(a)univpm.it&gt; wrote:

On Thu, 7 Jun 2007, Chris wrote: That's easy-peasy: when you compute the forecast errors e, just subtract from y the conditional mean too; clearly, you'll need to include the regressors as additional parameters to the function, as in function filter(series y, series x, \ scalar b, scalar arpar, scalar mapar, \ scalar om, scalar alpha, scalar beta, \ series *e, series *h) scalar err = 0 scalar T = $nobs series e = 0 series h = om/(1-alpha-beta) loop for i=2..T --quiet scalar e2lag = e[i-1]^2 # note the change here e[i] = y[i] - (x[i]*b + arpar*y[i-1] + mapar*e[i-1]) h[i] = om + alpha*e2lag + beta*h[i-1] end loop return scalar err end function Better still, you may want to specify x as a list (or a matrix) and b as a vector. Maybe it's time to get hold of a good econometrics textbook? ;-) Riccardo (Jack) Lucchetti Dipartimento di Economia Università Politecnica delle Marche r.lucchetti(a)univpm.it http://www.econ.univpm.it/lucchetti