Sim.Ar: Simulate from a reparametrized AR(2) model

In CarolinaEuan/HMClust: HMClust

Simulate from a reparametrized AR(2) model

Description

Simulate an AR(2) process with parameters M, and eta.

Usage

Sim.Ar(Time, eta, M, Fs=1, m_burn = 100)

Arguments

Time	Length of output series. A strictly positive integer.
eta	Peak frequency of the spectrum. eta must be less or equal than Fs/2.
M	Modulus of the roots of phi(z), where $z_0^1=Conj(z_0^2)$. M must be bigger than 1.
Fs	Sampling frequency (Hz). Default value is 1.
m_burn	Length of ‘burn-in’ period.

Details

In time series methods there exist some parametric models such as the autoregressive process of order $p$ (AR($p$)) that have a closed form for the spectral density. In particular the AR(2) model can be parametrized as a function of the norm of the root of its characteristic polynomial (M) and the peak frequency of the spectrum (eta). These parameters will determine the shape of the spectral density (peak and sparseness).

Value

A vector of length Time from an AR(2) model.

Examples

#Sim.Ar
eta<-2;M<-1.01;Fs<-10
Xt<-Sim.Ar(1000,eta,M,Fs)
fest<-spec.parzen(Xt,a=100,dt=1/Fs)
plot(seq(.1,100,.1),Xt,type="l",main="AR(2) Process",xlab="Time (sec)",ylab="")
plot(fest,type="l",lwd=2,main="Smoothed Periodogram",xlab="w (Hz)",ylab="")

CarolinaEuan/HMClust documentation built on Feb. 18, 2024, 10 p.m.