Wilkie model VARMA representation

[erinnc]

I am having trouble recreating the equity dividend yield equation (lnY(t)) in the Wilkiw model as it appears in the VARMA representation on pages 31-32 of Section 9 (Stochastic models of security prices).

Specifically I'm getting stuck on the co-efficient of QZ(t) which is shown in matrix B0 as QSD. I am getting YW.QSD.

I have not had any trouble getting to equation (2b) on age 28 of the notes;

lnY(t) = {YW.I(t) + lnYMU} + YA.[lnY(t-1) - {YW.I(t-1) + lnYMU}] + YSD.YZ(t)

From there I substitute the equation for I(t) and simplify / rearrange to find the coefficients for the matricies.

lnY(t) = {YW.[QMU+ ... + QSD.QZ(t)] + lnYMU} + ....

Because I(t); which is the source of the QZ(t) term, is multiplied by YW I can't see how it simplifies to QSD.QZ(t) alone?

I realise that this is probably going into detail which is beyond the scope of the course, but I've just gotten really stuck on this. Are you able to point out where I am going wrong?

Thanks
Erinn

 

[Mike Lewry]

I really wouldn't spend time on trying to recreate these matrices as they will not improve your understanding.

The Core Reading points out that the Wilkie model is used to illustrate some of the issues relevant to long-term risk management models. So you're not meant to be able to reproduce these matrices.

When I last attempted to do so and couldn't agree what was in the Core Reading, I raised it with the profession. They were surprised that anyone had attempted to reconcile these entries and said that as it is just illustrative it wasn't worth investigating further.

So I'd say you're probably not doing anything wrong.