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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{init_sys}{Linear polynomial model that configures the initial parameterization.
+Must be a BJ model. Overrules the \code{order} argument}
+
+\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] = \frac{B(q^{-1})}{F(q^{-1})}u[k-nk] + 
+   \frac{C(q^{-1})}{D(q^{-1})} e[k]
+}
+The orders of Box-Jenkins model are defined as follows:
+\deqn{
+   B(q^{-1}) = b_1 + b_2q^{-1} + \ldots + b_{nb} q^{-nb+1}
+}
+
+\deqn{
+   C(q^{-1}) = 1 + c_1q^{-1} + \ldots + c_{nc} q^{-nc}
+}
+
+\deqn{
+   D(q^{-1}) = 1 + d_1q^{-1} + \ldots + d_{nd} q^{-nd}
+}
+\deqn{
+   F(q^{-1}) = 1 + f_1q^{-1} + \ldots + f_{nf} q^{-nf}
+}
+
+The function estimates the coefficients using non-linear least squares 
+(Levenberg-Marquardt Algorithm)
+\cr
+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(bjsim,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
+}
+