specARIMA {longmemo} | R Documentation |
Calculate the spectral density of a fractional ARMA process with standard normal innovations and self-similarity parameter H.
specARIMA(eta, p, q, m)
eta |
parameter vector eta = c(H, phi, psi) . |
p, q |
integers giving AR and MA order respectively. |
m |
sample size determining Fourier frequencies. |
at the Fourier frequencies 2*π*j/n, (j=1,...,(n-1)), cov(X(t),X(t+k)) = (sigma/(2*pi))*integral(exp(iuk)g(u)du).
— or rather – FIXME –
1. cov(X(t),X(t+k)) = integral[ exp(iuk)f(u)du ]
2. f() = theta1 * f*() ; spec = f*(), and integral[log(f*())] = 0
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. |
pq |
a vector of length two, = c(p,q) . |
eta |
a named vector c(H=H, phi=phi, psi=psi) from input. |
method |
a character indicating the kind of model used. |
Jan Beran (principal) and Martin Maechler (fine tuning)
Beran (1994) and more, see ....
The spectral estimate for fractional Gaussian noise,
specFGN
.
In general, spectrum
and spec.ar
.
str(r.7 <- specARIMA(0.7, m = 256, p = 0, q = 0)) str(r.5 <- specARIMA(eta = c(H = 0.5, phi=c(-.06, 0.42, -0.36), psi=0.776), m = 256, p = 3, q = 1)) plot(r.7) plot(r.5)