Common factor model

[Karl]

Dear all,

my intention is to estimate a common factor model (still using EViews 5.1). Imagine two measurement series z1(k) and z2(k) (k=time index), both sharing a common component x(k) following AR(2). The other (idiosyncratic) components of z1(k) and z2(k) are disturbances with MA(1).

Estimating z1(k) and z2(k) separately is easy to accomplish - according to the handbook, I estimate for example (cc=common component):

@signal z1=cc1+c(1)*cc2
@state cc1=c(3)*cc1(-1)+c(4)*cc2(-1)+[var=exp(c(2))]
@state cc2=cc1(-1)

But how can an estimation be performed using both z1(k) and z2(k) (bearing in mind that there is a common component and different idiosyncratic disturbances). Has anybody an idea?

Thank you very much in advance. I appreciate your help,

Karl

[startz]

Add a signal equation for z2. You probably want an error term in both the z1 and z2 equations.

[Karl]

Thank you, Startz, for your reply. Unfortunately, adding a signal equation for z2 doesn't work ("near singular matrix" appears). The other thing is: z1 and z2 share the common component but differ in the disturbances' variance as in the MA(1) coefficients. May I draw your attention to the attached workfile?

[startz]

You haven't allowed an idiosyncratic component for either z1 or z2. You are also requiring that both have a unit loading on the common component, which is probably not what you want.

[Karl]

I need to ask for your assistance again. In the attached workfile you find another try to solve my problem. "SS12" estimates z1(k) and z2(k) separately, each following an ARIMA(2,0,1)-process. (I estimated this just as a kind of reference.) "SS13" modifies "SS12". Again, what I tried to do is: Estimating the common component of z1 and z2 as AR(2) allowing for different weights; estimating the idiosyncratic components as MA(1) with different variances and coefficients. I am not quite sure if the specification of "SS13" is in line with this.
Thank you again,
Karl