tar.skeleton {TSA}

Find the asympotitc behavior of the skeleton of a TAR model

Description

The skeleton of a TAR model is obtained by suppressing the noise term from the TAR model.

Usage

tar.skeleton(object, Phi1, Phi2, thd, d, p, ntransient = 500, n = 500, 
xstart, plot = TRUE,n.skeleton = 50)

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 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

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.

Value

A vector that contains the trajectory of the skeleton, with the burn-in discarded.

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

data(prey.eq)
prey.tar.1=tar(y=log(prey.eq),p1=4,p2=4,d=3,a=.1,b=.9,print=TRUE)
tar.skeleton(prey.tar.1)