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 skeleton trajectory
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
xstart
initial values for the iteration of the skeleton
plot
if True, the time series plot of the skeleton is drawn
n.skeleton
number of last n.skeleton points of the skeleton to be plotted
Value
A vector that contains the trajectory of the skeleton, with the burn-in
discarded.
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