chapter 35 UG II example armax(2,3) -state space models

[mandix]

I have a question that is killing me, and I am sure anybody of this forum can probably answer.
It is with regard to state space models, and the example in Chapter 35 of the Eviews User Guide II.
The example says:

**ARMAX(2, 3) with a Random Coefficient
We can use the syntax described above to define an ARMAX(2,3) with a random coefficient
for the regression variable X:
y = c(1) + sv5*x + sv1 + c(4)*sv2 + c(5)*sv3 + c(6)*sv4
@state sv1 = c(2)*sv1(-1) + c(3)*sv2(-1) + [var=exp(c(7))]
@state sv2 = sv1(-1)
@state sv3 = sv2(-1)
@state sv4 = sv3(-1)
@state sv5 = sv5(-1) + [var=3]
The AR coefficients are parameterized in terms of C(2) and C(3), while the MA coefficients
are given by C(4), C(5) and C(6). The variance of the innovation is restricted to be a positive
function of C(7). SV5 is the random coefficient on X, with variance restricted to be 3.** (End of quote)

What is killing me is this: *why* are the C(4), C(5) and C(6) coefficients the moving average (MA) coefficients?
They sound very much AR coefficients to me.
I know one can convert an MA(1) into an infinite AR, but I do not get why the claim on the C's in this example.
I ask, because if I check the same User Guide II, Chapter 26 on ARIMA theory, the treatment of the moving average part
is different (and so is the MA treatment in many textbooks on time series....).

Any hint for an answer is greatly appreciated.

Thanks so much, Manfred

[EViews Glenn]

I'm not quite sure the best way to answer the question. It might help to suppose that c(2) and c(3) are equal to zero. Then the states are the errors and the lags of the errors. I *think* that it's then pretty obvious why the coefficients are those for the MA...

[mandix]

Glenn, sorry, got caught up in work, and could not answer.
Listen, thanks. Your comment makes sense.

Manfred

[EViews Glenn]

No worries. "Thinking in state space" can sometimes be a bit different... Glad that my comment made sense.