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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/iv.R
\name{iv}
\alias{iv}
\title{ARX model estimation using instrumental variable method}
\usage{
iv(z, order = c(0, 1, 0), x = NULL)
}
\arguments{
\item{z}{an idframe object containing the data}
\item{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}
\item{x}{instrument variable matrix. x must be of the same size as the output
data. (Default: \code{NULL})}
}
\value{
An object of class \code{estpoly} containing the following elements:
\item{sys}{an \code{idpoly} object containing the
fitted ARX coefficients}
\item{fitted.values}{the predicted response}
\item{residuals}{the residuals}
\item{input}{the input data used}
\item{call}{the matched call}
\item{stats}{A list containing the following fields: \cr
\code{vcov} - the covariance matrix of the fitted coefficients \cr
\code{sigma} - the standard deviation of the innovations\cr
\code{df} - the residual degrees of freedom}
}
\description{
Estimates an ARX model of the specified order from input-output data using
the instrument variable method. If arbitrary instruments are not supplied
by the user, the instruments are generated using the arx routine
}
\details{
SISO ARX models are of the form
\deqn{
y[k] + a_1 y[k-1] + \ldots + a_{na} y[k-na] = b_{nk} u[k-nk] +
\ldots + b_{nk+nb} u[k-nk-nb] + e[k]
}
The function estimates the coefficients using linear least squares (with
regularization).
\cr
The data is expected to have no offsets or trends. They can be removed
using the \code{\link{detrend}} function.
}
\examples{
data(arxsim)
mod_iv <- iv(z,c(2,1,1))
}
\references{
Arun K. Tangirala (2015), \emph{Principles of System Identification:
Theory and Practice}, CRC Press, Boca Raton. Sections 21.7.1, 21.7.2
Lennart Ljung (1999), \emph{System Identification: Theory for the User},
2nd Edition, Prentice Hall, New York. Section 7.6
}
\seealso{
arx
}
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