specFGN {longmemo}R Documentation

Spectral Density of Fractional Gaussian Noise

Description

Calculation of the spectral density f of normalized fractional Gaussian noise with self-similarity parameter H at the Fourier frequencies 2*pi*j/m (j=1,...,(m-1)).

Usage

specFGN(eta, m, nsum = 200)

Arguments

eta parameter vector eta = c(H, *).
m sample size determining Fourier frequencies.
nsum length of approximating Riemans sum.

Details

Note that

  1. cov(X(t),X(t+k)) = integral[ exp(iuk)f(u)du ]
  2. f=theta1*spec and integral[log(spec)]=0.

Value

an object of class "spec" (see also spectrum) with components

freq the Fourier frequencies (in (0,π)) at which the spectrum is computed.
spec the scaled values spectral density f(λ) values at the freq values of λ.
f*(lambda) = f(lambda) / theta1 adjusted such int log(f^*(λ)) dλ = 0.
theta1 the scale factor theta_1.
H the self-similarity parameter from input.
method a character indicating the kind of model used.

Author(s)

Jan Beran (principal) and Martin Maechler (fine tuning)

References

Jan Beran (1994). Statistics for Long-Memory Processes; Chapman & Hall, NY.

Examples

 str(r.7  <- specFGN(0.7, m = 100))
 str(r.7f <- specFGN(0.7, m = 100, nsum = 10000))
 all.equal(r.7, r.7f)# different in about 5th digit only
 str(r.5  <- specFGN(0.5, m = 100))

 try(plot(r.7)) ## work around plot.spec() `bug' in R < 1.6.0
 plot(r.5, add = TRUE, col = "blue")

[Package longmemo version 0.9-6 Index]