View source: R/spectral_density.R
spectral.density | R Documentation |
Returns theoretical spectral density evaluated in ARMA and ARFIMA processes.
spectral.density(ar = numeric(), ma = numeric(), d = 0, sd = 1, lambda = NULL)
ar |
(type: numeric) AR vector. If the time serie doesn't have AR term then omit it. For more details see the examples. |
ma |
(type: numeric) MA vector. If the time serie doesn't have MA term then omit it. For more details see the examples. |
d |
(type: numeric) Long-memory parameter. If d is zero, then the process is ARMA(p,q). |
sd |
(type: numeric) Noise scale factor, by default is 1. |
lambda |
(type: numeric) |
The spectral density of an ARFIMA(p,d,q) processes is
f(\lambda) = \frac{\sigma^2}{2\pi} \cdot \bigg(2\,
\sin(\lambda/2)\bigg)^{-2d} \cdot
\frac{\bigg|\theta\bigg(\exp\bigg(-i\lambda\bigg)\bigg)\bigg|^2}
{\bigg|\phi\bigg(\exp\bigg(-i\lambda\bigg)\bigg)\bigg|^2}
With -\pi \le \lambda \le \pi
and -1 < d < 1/2
. |x|
is the
Mod
of x
. LSTS_sd
returns the
values corresponding to f(\lambda)
. When d
is zero, the spectral
density corresponds to an ARMA(p,q).
An unnamed vector of numeric class.
For more information on theoretical foundations and estimation methods see \insertRefbrockwell2002introductionLSTS \insertRefpalma2007longLSTS
# Spectral Density AR(1)
require(ggplot2)
f <- spectral.density(ar = 0.5, lambda = malleco)
ggplot(data.frame(x = malleco, y = f)) +
geom_line(aes(x = as.numeric(x), y = as.numeric(y))) +
labs(x = "Frequency", y = "Spectral Density") +
theme_minimal()
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