Constructor for LMFD (ARMA) Models

A left-matrix fraction description (LMFD) plus parameterisation of noise covariance.

Usage

armamod(sys, sigma_L = NULL, names = NULL, label = NULL)

Arguments

sys

rationalmatrices::lmfd() or rationalmatrices::rmfd() object

sigma_L

Left-factor of noise covariance, i.e. the covariance \(\sigma\) is obtained as sigma_L * t(sigma_L). If sigma_L is a vector of dimension \(n\), where \(n\) is the input dimension, only the diagonal elements are parametrized. If it is a vector of dimension \(n^2\), then the elements of sigma_L are filled column by column.

names

optional vector of character strings

label

optional character string

Value

Object of class armamod.

Details

In Hannan, Deistler (2012, page 7), RMFDs are also called dynamic adjustment forms. Internally, MFDs are lists with slots sys, sigma_L, names, label.

Examples

x = armamod(sys = lmfd(c(1, 0.5), 1), sigma_L = diag(1))
x
#> ARMA model [1,1] with orders p = 1 and q = 0
#> AR polynomial a(z):
#>      z^0 [,1] z^1 [,1]
#> [1,]        1      0.5
#> MA polynomial b(z):
#>      z^0 [,1]
#> [1,]        1
#> Left square root of noise covariance Sigma:
#>      u[1]
#> u[1]    1