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+% Generated by roxygen2 (4.1.1): do not edit by hand
+% Please edit documentation in R/estpoly.R
+\name{oe}
+\alias{oe}
+\title{Estimate Output-Error Models}
+\usage{
+oe(x, order = c(1, 0, 1))
+}
+\arguments{
+\item{x}{an object of class \code{idframe}}
+
+\item{order:}{Specification of the orders: the four integer components
+(nb,nf,nk) are order of polynomial B + 1, order of the polynomial F,
+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 output-error model of the specified order given the input-output data
+}
+\details{
+SISO OE models are of the form
+\deqn{
+   y[k] + f_1 y[k-1] + \ldots + f_{nf} y[k-nf] = b_{nk} u[k-nk] +
+   \ldots + b_{nk+nb} u[k-nk-nb] + f_{1} e[k-1] + \ldots f_{nf} e[k-nf]
+   + 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(oesim)
+z <- dataSlice(data,end=1533) # training set
+mod_oe <- oe(z,c(2,1,2))
+summary(mod_oe) # obtain estimates and their covariances
+plot(mod_oe) # 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, 17.5.2,
+21.6.3
+}
+