# spectral.density: Spectral Density In LSTS: Locally Stationary Time Series

## Description

Returns theoretical spectral density evaluated in ARMA and ARFIMA processes.

## Usage

 1 spectral.density(ar = numeric(), ma = numeric(), d = 0, sd = 1, lambda = NULL) 

## Arguments

 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) λ parameter on which the spectral density is calculated/computed. If lambda=NULL then it is considered a sequence between 0 and π.

## Details

The spectral density of an ARFIMA(p,d,q) processes is

f(λ) = \frac{σ^2}{2π} \cdot \bigg(2\, \sin(λ/2)\bigg)^{-2d} \cdot \frac{\bigg|θ\bigg(\exp\bigg(-iλ\bigg)\bigg)\bigg|^2} {\bigg|φ\bigg(\exp\bigg(-iλ\bigg)\bigg)\bigg|^2}

With -π ≤ λ ≤ π and -1 < d < 1/2. |x| is the Mod of x. LSTS_sd returns the values corresponding to f(λ). When d is zero, the spectral density corresponds to an ARMA(p,q).

## Value

An unnamed vector of numeric class.

## References

For more information on theoretical foundations and estimation methods see \insertRefbrockwell2002introductionLSTS \insertRefpalma2007longLSTS

## Examples

 1 2 3 4 5 6 7 # 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() 

LSTS documentation built on July 29, 2021, 5:07 p.m.