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+% Generated by roxygen2 (4.1.1): do not edit by hand
+% Please edit documentation in R/estpoly.R
+\name{arx}
+\alias{arx}
+\title{Estimate ARX Models}
+\usage{
+arx(data, order = c(0, 1, 0))
+}
+\arguments{
+\item{data}{an object of class \code{idframe}}
+
+\item{order:}{Specification of the orders: the three integer components
+(na,nb,nk) are the order of polynolnomial A, order of polynomial B and
+the input-output delay}
+}
+\value{
+An object with classes \code{estARX} and \code{estPoly}, containing
+the following elements:
+
+\tabular{ll}{
+   \code{coefficients} \tab an \code{idpoly} object containing the
+   fitted coefficients \cr
+   \code{vcov} \tab the covariance matrix of the fitted coefficients\cr
+   \code{sigma} \tab the standard deviation of the innovations\cr
+   \code{df} \tab the residual degrees of freedom \cr
+   \code{fitted.values} \tab the predicted response \cr
+   \code{residuals} \tab the residuals  \cr
+   \code{call} \tab the matched call \cr
+   \code{time} \tab the time of the data used \cr
+   \code{input} \tab the input data used
+ }
+}
+\description{
+Fit an ARX model of the specified order given the input-output data
+}
+\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
+no regularization). Future versions may include regularization
+parameters as well
+\\
+The data is expected to have no offsets or trends. They can be removed
+using the \code{\link{detrend}} function.
+}
+\examples{
+data(arxsim)
+model <- arx(data,c(2,1,1))
+summary(model) # obtain estimates and their covariances
+plot(model) # plot the predicted and actual responses
+}
+\references{
+Arun K. Tangirala (2015), \emph{Principles of System Identification:
+Theory and Practice}, CRC Press, Boca Raton. Section 21.6.1
+
+Lennart Ljung (1999), \emph{System Identification: Theory for the User},
+2nd Edition, Prentice Hall, New York. Section 10.1
+}
+