timsac (version 1.3.8)

raspec: Rational Spectrum

Description

Compute power spectrum of ARMA process.

Usage

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

Value

raspec gives the rational spectrum.

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.

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))