Restricting model coefficients

[Fmuskens]

Hi,

I have a question about estimating the coefficients of the following model:
Q_t=(1-α-β)Q + α u_(t-1)^2 + β Q_(t-1)

where
Q = sample mean of Q_t
u_t = error term (obtained from a model estimated previously)

α and β are the coefficients of the model

The above stated equation is the last step in a DCC-GARCH bivariate model. It is a mean-reverting process of Variances and Covariances. I estimate it using Maximum Likelihood.
My question is the following:
How can I restrict the coefficients such that
α > 0
β > 0
(α+β) < 1

I found some solutions on restricting α > 0 and β > 0, by using exp(α) and exp(β). But I could not find a solution on how to restrict (α+β) < 1, and when this is possible, how to combine the three restrictions.

If anyone could give me some advice, I would be really grateful.

Thanks in advance.

[EViews Gareth]

http://forums.eviews.com/viewtopic.php?f=4&t=48&p=99

[Fmuskens]

Thank you for your reply, but I already read that post and could not find a solution for my problem:
α > 0
β > 0
(α+β) < 1

I did find an answer for
α > 0
β > 0
(α+β) = 1
That is,

Code: Select all

ai = exp( bi ) / ( exp( b1 ) + exp( b2 ) + ... + exp( bk ) )

But that's unfortunately not what I'm looking for. Is there a way to adjust this code:
Or can I restrict the coefficients in another way?