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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/estpoly.R
\name{bj}
\alias{bj}
\title{Estimate Box-Jenkins Models}
\usage{
bj(z, order = c(1, 1, 1, 1, 0), init_sys = NULL, options = optimOptions())
}
\arguments{
\item{z}{an \code{idframe} object containing the data}
\item{order}{Specification of the orders: the five integer components
(nb,nc,nd,nf,nk) are order of polynomial B + 1, order of the polynomial C,
order of the polynomial D, order of the polynomial F, and the
input-output delay respectively}
\item{options}{Estimation Options, setup using
\code{\link{optimOptions}}}
}
\value{
An object of class \code{estpoly} containing the following elements:
\item{sys}{an \code{idpoly} object containing the
fitted BJ 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}
\item{options}{Option set used for estimation. If no
custom options were configured, this is a set of default options}
\item{termination}{Termination conditions for the iterative
search used for prediction error minimization:
\code{WhyStop} - Reason for termination \cr
\code{iter} - Number of Iterations \cr
\code{iter} - Number of Function Evaluations }
}
\description{
Fit a box-jenkins model of the specified order from input-output data
}
\details{
SISO BJ 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(bjsim)
z <- dataSlice(data,end=1500) # training set
mod_bj <- bj(z,c(2,1,1,1,2))
mod_bj
residplot(mod_bj) # residual plots
}
\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
}
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