% 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 C,and the input-output delay respectively}
}
\value{
An object of class \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 ARMAX 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 non-linear least squares
(Levenberg-Marquardt Algorithm)
\\
The data is expected to have no offsets or trends. They can be removed
using the \code{\link{detrend}} function.
}
\examples{
data(armaxsim)
z <- dataSlice(data,end=1533) # training set
mod_armax <- armax(z,c(1,2,1,2))
summary(mod_armax) # obtain estimates and their covariances
plot(mod_armax) # 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
}