data.gen.tar {synthesis}

Generate a two-regime threshold autoregressive (TAR) process.

Description

Generate a two-regime threshold autoregressive (TAR) process.

Usage

data.gen.tar(
  nobs,
  ndim = 9,
  phi1 = c(0.6, -0.1),
  phi2 = c(-1.1, 0),
  theta = 0,
  d = 2,
  p = 2,
  noise = 0.1
)

Arguments

nobs

the data length to be generated

ndim

The number of potential predictors (default is 9)

phi1

the coefficient vector of the lower-regime model

phi2

the coefficient vector of the upper-regime model

theta

threshold

d

delay

p

maximum autoregressive order

noise

the white noise in the data

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}+\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} Y_{t-p}+\sigma_2 e_t, \mbox{ if } Y_{t-d} > r.

where r is the threshold and d the delay.

Value

A list of 2 elements: a vector of response (x), and a matrix of potential predictors (dp) with each column containing one potential predictor.

References

Cryer, J. D. and K.-S. Chan (2008). Time Series Analysis With Applications in R Second Edition Springer Science+ Business Media, LLC.

Examples

# TAR2 model from paper with total 9 dimensions
data.tar<-data.gen.tar(500)
plot.ts(cbind(data.tar$x,data.tar$dp))