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+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/estpoly.R
+\name{arx}
+\alias{arx}
+\title{Estimate ARX Models}
+\usage{
+arx(x, order = c(1, 1, 1), lambda = 0.1, intNoise = FALSE, fixed = NULL)
+}
+\arguments{
+\item{x}{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 + 1) and 
+the input-output delay}
+
+\item{lambda}{Regularization parameter(Default=\code{0.1})}
+
+\item{intNoise}{Logical variable indicating whether to add integrators in
+the noise channel (Default=\code{FALSE})}
+
+\item{fixed}{list containing fixed parameters. If supplied, only \code{NA} entries 
+will be varied. Specified as a list of two vectors, each containing the parameters
+of polynomials A and B respectively.}
+}
+\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{
+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
+regularization).
+\cr
+The data is expected to have no offsets or trends. They can be removed 
+using the \code{\link{detrend}} function. 
+\cr
+To estimate finite impulse response(\code{FIR}) models, specify the first
+order to be zero.
+}
+\examples{
+data(arxsim)
+mod_arx <- arx(arxsim,c(1,2,2))
+mod_arx
+plot(mod_arx) # 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
+}
+