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Posted: **Sat Dec 19, 2015 3:38 pm**

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

Posted: **Sun Dec 20, 2015 3:41 pm**

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.

Posted: **Sun Dec 20, 2015 7:17 pm**

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

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Airline Model in sspace form

Airline Model in sspace form

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Re: Airline Model in sspace form