State Space Uncorrelated Intertemporal Errors

[praktikantzew]

Hey Eviews-Helpers,

I would like to estimate a state space model using Eviews looking like this:
@signal fra_agric_g = c(4) + c(5)*sv1 + e1
@signal fra_constr_g = c(7) + c(8)*sv1 + e2
@signal fra_finance_g = c(10) + c(11)*sv1 + [var = exp(c(12))]
@signal fra_industry_g = c(13) + c(14)*sv1 + [var = exp(c(15))]
@signal fra_public_g = c(16) + c(17)*sv1 + [var = exp(c(18))]
@signal fra_trade_g = c(19) + c(20)*sv1 + [var = exp(c(21))]

@state sv1 = c(1)*sv1(-1) + c(2)*sv2(-1) + [var = exp(c(3))]
@state sv2 = sv1(-1)

@ename e1
@ename e2
@evar var(e1) = exp(c(6))
@evar var(e2) = exp(c(9))
@evar cov(e1,e2) = 0

The estimation works fine,but I have 2 problems:

I know that the error terms are by default uncorrelated with each other and thus the last line is redundant.

1)
However, for my model it is also necessary to make sure that the errors are intertemporally uncorrelated, meaning cov(e_t,e_(t+i))=0.
Is this also the default setting in Eviews or can I specify this somehow?

2) Another scenario:
The Eviews Help Guide states that the state equation is modelled like a lead.
This means that when I want to allow for correlation between the errorterms of the signal and state equation I have to be careful about the timing:

"The timing in the signal equation and state equation implies that correlation between the signal and state errors is defined to be between the
errors in the signal at time t , and the errors in the states dated in t+1 . This timing may
not be what you intend. To allow for correlation in the contemporaneous states and signals
in time , you will need to specify errors in the lagged states, and define correlation
between the lagged state errors and the errors in the signal equation."

The question is: How do I specify the correlation with regard to the timing so that I really get the correlation of E_t and V_t instead of E_t and V_(t+1) ?

Thank you so much in advance, I hope I made my questions clear.

[trubador]

1) You do not have to specify it explicitly since standard Kalman filter assumes that errors are independent and identically distributed normal random variables. However, if your model is ill-defined or misspecified then error terms might not satisfy that condition, so you better check the diagnostics for residuals after the estimation.
2) Suppose you want to define a correlation between the first signal variable and the first state variable:

Code: Select all

... @state sv1 = c(1)*sv1(-1) + c(2)*sv2(-1) + noise(-1) @state sv2 = sv1(-1) @state noise = [ename=es1,var=exp(c(3))] ... @evar cov(e1,es1) = c(22)