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# Difficulty with GARCH-M-ARMA MODEL

Hi,

I am trying to incorporate the ARMA(2,3) model with the GARCH(1,1) model in the main equation (ARMA(2,3)+GARCH(1,1)) to predict the wind speed. My equation is as follows;

y=mu+ar1*(y(t-1))+ar2*y(t-2))+ma1*(resid.y(t-1))+ma2*(resid.y(t-2))+ma3*(resid.y(t-3))+gamma*sqrt(var(y)) (garch-m model)

var(y) is calculated as follows

var(y)=arch0+arch1*(resid.y(t-1)^2)+garch1*(var(y(t-1))) (i.e. garch component)

y is the historical hourly wind speed over 3 month period. I keep it in Excel in a single column with a row header named y and import it in SAS.

I try to represent the equations in SAS and submit the following code

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proc model data = Erman maxiter=1000;

h.y = arch0 + arch1 * xlag(resid.y ** 2,mse.y) + garch1 * xlag(h.y,mse.y);

y = mu + ar1 * zlag1(y - mu) + ar2 * zlag2(y-mu) + ma1 * zlag1(resid.y)+ ma2 * zlag2(resid.y) + ma3 * zlag3(resid.y)+gamma*(sqrt(h));

h.y=h;

PARMS ar1 1.725 ar2 -0.543 ma1 0.831 ma2 0.122 ma3 -0.04 mu 3.899 arch0 0.5 arch1 0.5 garch1 0.5 gamma 0.5 ;
fit y / method = marquardt fiml;

quit;

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In return the SAS returned the following results

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Parameter Estimate Std Err t Value Pr > |t|

arch0 0.5 0 . .
arch1 0.5 0 . .
garch1 0.5 0 . .
mu -4.15485 0.4568 <------ Biased
ar1 1.660557 0.0152 <------ Biased
ar2 -0.67302 0.0146 <------ Biased
ma1 0.762798 0.0163 <------ Biased
ma2 0.147934 0.00529 <------ Biased
ma3 -0.04542 0.00746 <------ Biased
gamma 0.068962 0 <------ Biased
h 2.109533 0.0121 <------ Biased

NOTE: The model was singular. Some estimates are marked 'Biased'.

Number of Observations Statistics for System

Used 2250 Log Likelihood -109853
Missing 0

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Why this message comes up, it says the estimates biased, and although the model converged, the initial values for arch0, arch1, garch1 parameters have not changed. I tried it with different values but same results come up

It says the model was singular. If anybody can help regarding this issue, how to obtain a nonbiased estimates and not a singular model, I will be glad. Thanks. I am using SAS 9.1. version

Regards
Erman
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