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hello!

i wanted to ask somebody, i am having trouble with finding out this:

when i add variables into the variance equation, the estimated parameters... do i have to put a constraint on them, i.e. see if the estimated parameter is valid.
because when you have a normal garch, without additional variables in the variance equation, then in order to variance be a finite one, the sum of estimated paramters has to be less than 1. (almost all books on garch show why this has to be equal less than 1).
my quetion is, when i add additional variables, what sign do estimated parameters have to have? or is it the sum of the parameters? or something else?
i'm trying to figure it out but having trouble..

books don't give this answers, but papers i have been reading which have been empirically dealing with this do not give me the answer also. they just interpret the estimated parameters. but i think there shoud be some restrictions. first of all, the conditional variance has to be positive. this is something we all know. but, if you estimate an equation and get parameters with which you get a negative conditional variance then you know you shoudn't use those variables which cause the problems.
or am i wrong?
please help (or/and discuss)

anyone, please: (

GARCH is a very powerful technique and therefore you do not need to intervene in the estimation process most of the time. When putting restrictions, you should be extremely careful since it complicates parameter estimation process. If your model is converged properly but does not meet the assumptions, then you can change either the sample period or specification of your model. On the other hand, if your model is not converged properly, then you may be experiencing some kind of parameter instability. In that case, you can try different options for the optimization procedure (e.g. remove backcasting, use different algorithm, alter convergence criteria, etc.). If none of these work, then again it may be due to an ill-defined model.