Signal-to-noise ratio

[jons]

Hello,

I’m trying to replicate a state space model which, when simplified, consists of one signal equation and one state equation. The state equation is a random walk and there is a signal-to-noise ratio relating the standard deviation (not the variance) of the error terms of the two equations. However, I’m not sure how to write this signal-to-noise ratio in the Eviews state space object.

The signal equation is:
@signal ser01 = c(1)*ser01(-1) + c(2)*sv01(-1) + [var=exp(c(3))]

The state equation is:
@state sv01 = sv01(-1) + [var=exp(c(4))]

If we call sigma3 the standard deviation of the error term of the signal equation and sigma4 that of the state equation, the signal-to-noise ratio must be equal to:
Lambda = (sigma4 * c(2))/(sigma3 * 2^0.5)
Hence:
Sigma4 = sigma3*((lambda*2^0.5)/c(2))

In this case, am I correct to rewrite the state equation as follows?
@state sv01 = sv01(-1) + [var=exp(c(3))*((lambda*2^0.5)/c(2))^2]

Thanks for your help

[trubador]

Yes, that is correct.