iv4: ARX model estimation using four-stage instrumental variable...
In sysid: System Identification in R

Description Usage Arguments Details Value References See Also Examples

Estimates an ARX model of the specified order from input-output data using the instrument variable method. The estimation algorithm is insensitive to the color of the noise term.

1	iv4(z, order = c(0, 1, 0))

`z`	an idframe object containing the data
`order`	Specification of the orders: the three integer components (na,nb,nk) are the order of polynolnomial A, (order of polynomial B + 1) and the input-output delay

Estimation is performed in 4 stages. The first stage uses the arx function. The resulting model generates the instruments for a second-stage IV estimate. The residuals obtained from this model are modeled using a sufficently high-order AR model. At the fourth stage, the input-output data is filtered through this AR model and then subjected to the IV function with the same instrument filters as in the second stage.

An object of class estpoly containing the following elements:

`sys`	an `idpoly` object containing the fitted ARX coefficients
`fitted.values`	the predicted response
`residuals`	the residuals
`input`	the input data used
`call`	the matched call
`stats`	A list containing the following fields: `vcov` - the covariance matrix of the fitted coefficients `sigma` - the standard deviation of the innovations `df` - the residual degrees of freedom

Lennart Ljung (1999), System Identification: Theory for the User, 2nd Edition, Prentice Hall, New York. Section 15.3

arx, iv4

mod_dgp <- idpoly(A=c(1,-0.5),B=c(0.6,-.2),C=c(1,0.6),ioDelay = 2,noiseVar = 0.1)
u <- idinput(400,"prbs")
y <- sim(mod_dgp,u,addNoise=TRUE)
z <- idframe(y,u)
mod_iv4 <- iv4(z,c(1,2,2))