timsac (version 1.3.0)

raspec: Rational Spectrum

Description

Compute power spectrum of ARMA process.

Usage

raspec(h, var, arcoef=NULL, macoef=NULL, log=FALSE, plot=TRUE)

Arguments

h

specify frequencies $i$/2h ($i=0,1,\ldots,$h).

var

variance.

arcoef

AR coefficients.

macoef

MA coefficients.

log

logical. If TRUE the spectrum is plotted as log(raspec).

plot

logical. If TRUE (default) the spectrum is plotted.

Value

• raspec gives the rational spectrum.

Details

ARMA process : $$y(t) - a(1)y(t-1) - \ldots - a(p)y(t-p) = u(t) - b(1)u(t-1) - \ldots - b(q)u(t-q)$$ where $p$ is AR order, $q$ is MA order and $u(t)$ is a white noise with zero mean and variance equal to var.

References

H.Akaike and T.Nakagawa (1988) Statistical Analysis and Control of Dynamic Systems. Kluwer Academic publishers.

Examples

# Example 1 for the AR model
  raspec(h=100, var=1, arcoef=c(0.64,-0.8))

  # Example 2 for the MA model
  raspec(h=20, var=1, macoef=c(0.64,-0.8))