periodogram: Periodogram function

In pachamaltese/lsts: Locally Stationary Time Series

Periodogram function

Description

This function computes the periodogram from a stationary time serie. Returns the periodogram, its graph and the Fourier frequency.

Usage

periodogram(y, plot = TRUE, include.taper = FALSE)

Arguments

y	(type: numeric) data vector
plot	(type: logical) logical argument which allows to plot the periodogram. Defaults to TRUE.
include.taper	(type: logical) logical argument which by default is FALSE. If include.taper=TRUE then y is multiplied by 0.5(1 - \cos(2\pi(n-1)/n)) (cosine bell).

Details

The tapered periodogram it is given by

I(\lambda) = \frac{|D_n(\lambda)|^2}{2\pi H_{2,n}(0)}

with D(\lambda) = \sum_{s=0}^{n-1} h \left(\frac{s}{N}\right) y_{s+1}\, e^{-i\,\lambda\,s}, H_{k,n} = \sum_{s=0}^{n-1}h \left(\frac{s}{N}\right)^k\, e^{-i\,\lambda\,s} and \lambda are Fourier frequencies defined as 2\pi k/n, with k = 1,\,\ldots,\, n. The data taper used is the cosine bell function, h(x) = \frac{1}{2}[1-\cos(2\pi x)]. If the series has missing data, these are replaced by the average of the data and n it is corrected by $n-N$, where N is the amount of missing values of serie. The plot of the periodogram is periodogram values vs. \lambda.

Value

A list with with the periodogram and the lambda values.

References

For more information on theoretical foundations and estimation methods see \insertRefbrockwell2002introductionLSTS \insertRefdahlhaus1997fittingLSTS

See Also

fft, Mod, smooth.spline.

Examples

# AR(1) simulated
set.seed(1776)
ts.sim <- arima.sim(n = 1000, model = list(order = c(1, 0, 0), ar = 0.7))
per <- periodogram(ts.sim)
per$plot

pachamaltese/lsts documentation built on Jan. 27, 2024, 4:39 a.m.