omega {weakARMA}

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

y <- sim.ARMA(n = 1000, ar = c(0.95,-0.8), ma = -0.6)
est<-estimation(p = 2, q = 1, y = y)
omega(ar = est$ar, ma = est$ma, y = y)

estCAC<-estimation(p = 1, q = 1, y = CAC40return.sq, meanparam = TRUE)
omega(ar = estCAC$ar, ma = estCAC$ma, y = CAC40return.sq)