# tar.skeleton: Find the asympotitc behavior of the skeleton of a TAR model In TSA: Time Series Analysis

## Description

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

## Usage

 ```1 2``` ```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 = 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 vector that contains the trajectory of the skeleton, with the burn-in discarded.

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

`tar`
 ```1 2 3``` ```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) ```