diff options
Diffstat (limited to 'man')
| -rw-r--r-- | man/estARX.Rd | 22 |
1 files changed, 16 insertions, 6 deletions
diff --git a/man/estARX.Rd b/man/estARX.Rd index d4ff9b6..11858f8 100644 --- a/man/estARX.Rd +++ b/man/estARX.Rd @@ -22,8 +22,8 @@ the following elements: 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} the residual degrees of freedom\tab \cr - \code{fitted.values} \tab the predicted response + \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 @@ -33,7 +33,17 @@ the following elements: Fit an ARX model of the specified order given the input-output data } \details{ -ARX models are of the form \\ +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] + 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) @@ -42,10 +52,10 @@ summary(model) # obtain estimates and their covariances plot(model) # plot the predicted and actual responses } \references{ -Arun K. Tangirala (2015), Principles of System Identification: Theory and -Practice, CRC Press, Boca Raton. Section 21.6.1 +Arun K. Tangirala (2015), \emph{Principles of System Identification: +Theory and Practice}, CRC Press, Boca Raton. Section 21.6.1 -Lennart Ljung (1999) System Identification: Theory for the User, +Lennart Ljung (1999), \emph{System Identification: Theory for the User}, 2nd Edition, Prentice Hall, New York. Section 10.1 } |