diff options
| -rw-r--r-- | R/estpoly.R | 21 | ||||
| -rw-r--r-- | man/bj.Rd | 21 |
2 files changed, 36 insertions, 6 deletions
diff --git a/R/estpoly.R b/R/estpoly.R index 96add69..7d85408 100644 --- a/R/estpoly.R +++ b/R/estpoly.R @@ -383,10 +383,25 @@ oe <- function(x,order=c(1,1,0),options=optimOptions()){ #' @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] +#' 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) #' \\ @@ -42,10 +42,25 @@ 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] + 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) \\ |