I am a grad student in statistics

at Penn State University and

I have the following time-series problem that

i have been working on for a while with

no luck. Eevn if anyone can tell

me that it is not possible to solve

a problem like this, this is

fine also. Atleast I will know

that I should stop trying.

thanks.

Here's the problem :

I have the following MA(5) model ( this is the model
you get if you write Harvey's bsm in the single
source of error form but that doesn't matter ) :

y_t = epslion_t + (alpha1 + alpha2 - alpha3 -1)*epsilon_t-1

+ (alpha2+alpha3)*epsilon_t-2 + (alpha2)*epsilon_t-3

+ (alpha2 + alpha3-1)*epsilon_t-4 + (1-alpha1-alpha3)*epsilon_t-5.

So, it is an MA(5) model but it only has 3 unknown parameters.

I usually use ox to estimate ma models but for this
special ma model,
I think I can write the likelihood myself and then estimate the parameters
by, say, minimizing the residual variance in the likelhood etc.
my problem is
the following : I have noticed in the software package called
ox, if they get non invertible ma parameters after the minimization
, they then deal with the invertibility issue by
finding the inverse
roots which are greater than 1, flipping these roots, and then
rebuilding the ploynomial. ( they have functions like
polyroots which finds the roots and polymake which
can rebuild the polynomial given the new roots ). I
think that they can do this because they don't have this dependence
between the parameters that I have. I don't think I
can do what they do, in terms of fixing the invertibility
problem, because of the dependence between my parameters ?

I can flip the roots but when I reconstruct the polynomial

using polymake I will lose the relationships.

If I am correct in what is say, do you think it is possible

in some way to estimate an invertible model of this strange type ? I
really appreciate your answer. thank you
very much for taking the time to read this.
I really appreciate your help.

Mark