tar.sim: Simulate a two-regime TAR model

In TSA: Time Series Analysis

Simulate a two-regime TAR model

Description

Simulate a two-regime TAR model.

Usage

tar.sim(object, ntransient = 500, n = 500, Phi1, Phi2, thd, d, p, sigma1, 
sigma2, xstart = rep(0, max(p,d)), e)

Arguments

object	a TAR model fitted by the tar function; if it is supplied, the model parameters and initial values are extracted from it
ntransient	the burn-in size
n	sample size of the simulated series
Phi1	the coefficient vector of the lower-regime model
Phi2	the coefficient vector of the upper-regime model
thd	threshold
d	delay
p	maximum autoregressive order
sigma1	noise std. dev. in the lower regime
sigma2	noise std. dev. in the upper regime
xstart	initial values for the simulation
e	standardized noise series of size equal to length(xstart)+ntransient+n; if missing, it will be generated as some normally distributed errors

Details

The two-regime Threshold Autoregressive (TAR) model is given by the following formula:

Y_t = φ_{1,0}+φ_{1,1} Y_{t-1} +…+ φ_{1,p} Y_{t-p_1} +σ_1 e_t, \mbox{ if } Y_{t-d}≤ r

Y_t = φ_{2,0}+φ_{2,1} Y_{t-1} +…+φ_{2,p_2} Y_{t-p}+σ_2 e_t, \mbox{ if } Y_{t-d} > r.

where r is the threshold and d the delay.

Value

A list containing the following components:

y	simulated TAR series
e	the standardized errors

...

Author(s)

Kung-Sik Chan

References

Tong, H. (1990) "Non-linear Time Series, a Dynamical System Approach," Clarendon Press Oxford "Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan

See Also

tar

Examples

set.seed(1234579)
y=tar.sim(n=100,Phi1=c(0,0.5),
Phi2=c(0,-1.8),p=1,d=1,sigma1=1,thd=-1,
sigma2=2)$y
plot(y=y,x=1:100,type='b',xlab="t",ylab=expression(Y[t]))

TSA documentation built on July 5, 2022, 5:05 p.m.