Airline Model in sspace form

[xprimexinverse]

Hi,

I am trying to learn the EViews syntax for specifying state-space models.

I'm following the Seasonal ARIMA(0,1,1)(0,1,1) (airline model) example from the EViews example programs.

The relevant code is shown below.

Code: Select all

'airline model transformation series y = dlog(x,1,12) 'setup ARMA(0,1)(0,1) in sspace sspace ss1 ss1.append @signal y = sv1 + c(1)*sv2 + c(2)*sv13 + c(1)*c(2)*sv14 ss1.append @state sv1 = [var = exp(c(3))] ss1.append @state sv2 = sv1(-1) ss1.append @state sv3 = sv2(-1) ss1.append @state sv4 = sv3(-1) ss1.append @state sv5 = sv4(-1) ss1.append @state sv6 = sv5(-1) ss1.append @state sv7 = sv6(-1) ss1.append @state sv8 = sv7(-1) ss1.append @state sv9 = sv8(-1) ss1.append @state sv10 = sv9(-1) ss1.append @state sv11 = sv10(-1) ss1.append @state sv12 = sv11(-1) ss1.append @state sv13 = sv12(-1) ss1.append @state sv14 = sv13(-1)

I am seeking an explanation of the following term in the measurement (signal) equation; c(1)*c(2)*sv14. What does this term represent?

Just so we're on the same page, my understanding so far is in bullet points below.

• series y = dlog(x,1,12) implements both non-seasonal and seasonal differencing, or d = 1 and D = 1, with period s = 12.
• sv1 is an error term (state variable with variance to be estimated).
• sv2 to sv14 are somewhat artificial state variables for creating lagged (more than once) variables.
• sv2 is the non-seasonal MA(1) term, or q = 1.
• sv13 is the seasonal MA(1) term, or Q = 1.

Each of the seven parameters in the ARIMA(p,d,q)(P,D,Q)[s] notation seems to be accounted for. This leaves c(1)*c(2)*sv14 outstanding? What am I missing?

Cheers,
Graeme

[trubador]

Seasonal MA(12) model is as follows: Yt=[1+c(1)*L]*[1+c(2)*L^12]*et
which can be expanded as: Yt = et + c(1)*et-1 + c(2)*et-12 + c(1)*c(2)*et-13
Defining a state variable like SV{k} = SV(-k) for k>1 is not possible within the state space framework. Therefore, one needs to augment the states in order to cast such a model into the state space form.
Since SV1 is defined as et, SV13 and SV14 correspond to et-12 and et-13, respectively.

[xprimexinverse]

trubador,

Ah, of course!

I kept thinking of the notation for the additive form - overlooking the multiplicative form.

Now I see it. Clear as day.

Thanks,
Graeme