tar.skeleton function

Find the asympotitc behavior of the skeleton of a TAR model

Find the asympotitc behavior of the skeleton of a TAR model

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

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:

Yt=ϕ1,0+ϕ1,1Yt−1+…+ϕ1,pYt−p1+σ1et,\mboxifYt−d≤r 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 Yt=ϕ2,0+ϕ2,1Yt−1+…+ϕ2,p2Yt−p+σ2et,\mboxifYt−d>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.

Returns

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

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

Author(s)

Kung-Sik 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)
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