timsac (version 1.3.8)

mulspe: Multiple Spectrum

Description

Compute multiple spectrum estimates using Akaike window or Hanning window.

Usage

mulspe(y, lag = NULL, window = "Akaike", plot = TRUE, plot.scale = FALSE)

Value

spec

spectrum smoothing by 'window'.

Lower triangular parts :	Real parts
Upper triangular parts :	Imaginary parts

stat

test statistics.

coh

simple coherence by 'window'.

Arguments

y

a multivariate time series with \(d\) variables and \(n\) observations.

lag

maximum lag. Default is \(2 \sqrt{n}\), where \(n\) is the number of observations.

window

character string giving the definition of smoothing window. Allowed strings are "Akaike" (default) or "Hanning".

plot

logical. If TRUE (default) spectrums are plotted as \((d,d)\) matrix.

Diagonal parts :	Auto spectrums for each series.
Lower triangular parts :	Amplitude spectrums.
Upper triangular part :	Phase spectrums.

plot.scale

logical. IF TRUE, the common range of the \(y\)-axis is used.

Details

Hanning Window :	a1(0)=0.5,	a1(1)=a1(-1)=0.25,	a1(2)=a1(-2)=0
Akaike Window :	a2(0)=0.625,	a2(1)=a2(-1)=0.25,	a2(2)=a2(-2)=-0.0625

References

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

Examples

sgnl <- rnorm(1003)
x <- matrix(0, nrow = 1000, ncol = 2)
x[, 1] <- sgnl[4:1003]
# x[i,2] = 0.9*x[i-3,1] + 0.2*N(0,1)
x[, 2] <- 0.9*sgnl[1:1000] + 0.2*rnorm(1000)
mulspe(x, lag = 100, window = "Hanning", plot.scale = TRUE)