iv4 {sysid}

ARX model estimation using four-stage instrumental variable method

Description

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.

Usage

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

Arguments

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

Details

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.

Value

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

References

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

See Also

arx, iv4

Examples

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))