tar.skeleton: Find the asympotitc behavior of the skeleton of a TAR model

In TSA: Time Series Analysis

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 = 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.

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)

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