weakARMA (version 1.0.3)

omega: Computation of Fisher information matrice

Description

Computes matrices of Fisher information like \(I\), \(J\).

Usage

omega(ar = NULL, ma = NULL, y)

Arguments

ar

Vector of AR coefficients. If NULL, the simulation is a MA process.

ma

Vector of MA coefficients. If NULL, the simulation is a AR process.

y

Univariate time series.

Value

A list of matrix containing:

I

Matrix I computed in function matXi.

J

Matrix J computed as \(\frac{2}{n} H(e) H(e)^t \) where \(e\) is the residuals vector.

J.inv

Inverse of the matrix J.

matOmega

Matrix variance-covariance in the weak case computed as \(J^{-1}IJ^{-1}\).

matvar.strong

Matrix variance-covariance in the strong case computed as \(2\sigma^2J^{-1}\).

standard.dev.Omega

Standard deviation of the matrix matOmega.

standard.dev.strong

Standard deviation of the matrix matvar.strong.

sig2

Innovation variance estimate.

Examples

# NOT RUN {
y <- sim.ARMA(n = 1000, ar = c(0.95,-0.8), ma = -0.6)
# }
# NOT RUN {
est<-estimation(p = 2, q = 1, y = y)
# }
# NOT RUN {
omega(ar = est$ar, ma = est$ma, y = y)
# }
# NOT RUN {
estCAC<-estimation(p = 1, q = 1, y = CAC40return.sq, meanparam = TRUE)
# }
# NOT RUN {
omega(ar = estCAC$ar, ma = estCAC$ma, y = CAC40return.sq)
# }