% Generated by roxygen2 (4.1.1): do not edit by hand
% Please edit documentation in R/estpoly.R
\name{armax}
\alias{armax}
\title{Estimate ARMAX Models}
\usage{
armax(x, order = c(0, 1, 1, 0))
}
\arguments{
\item{x}{an object of class \code{idframe}}

\item{order:}{Specification of the orders: the four integer components
(na,nb,nc,nk) are the order of polynolnomial A, order of polynomial B
+ 1, order of the polynomial,and the input-output delay respectively}
}
\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 ARMAX 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] + c_{1} e[k-1] + \ldots c_{nc} e[k-nc]
   + 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 <- armax(data,c(1,2,1,2))
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. Sections 14.4.1, 21.6.2
}