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
Value
A list containing the following components:
y
simulated TAR series
e
the standardized errors
...
Details
The two-regime Threshold Autoregressive (TAR) model is given by the following
formula:
$$
Y_t = \phi_{1,0}+\phi_{1,1} Y_{t-1} +\ldots+ \phi_{1,p} Y_{t-p_1} +\sigma_1 e_t,
\mbox{ if } Y_{t-d}\le r $$
$$ Y_t = \phi_{2,0}+\phi_{2,1} Y_{t-1} +\ldots+\phi_{2,p_2} Y_{t-p}+\sigma_2 e_t,
\mbox{ if } Y_{t-d} > r.$$
where r is the threshold and d the delay.
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
# NOT RUN {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]))
# }