simu.tar.lognorm {TAR}

Simulate a series from a log-normal TAR model with Gaussian distributed error for positive valued time series.

Description

This function simulates a serie from a log-normal TAR model with Gaussian distributed error given the parameters of the model from a given threshold process \{Z_t\}

Usage

simu.tar.lognorm(Z, l, r, K, theta, H)

Arguments

Z

The threshold series

l

The number of regimes.

r

The vector of thresholds for the series \{Z_t\}.

K

The vector containing the autoregressive orders of the l regimes.

theta

The matrix of autoregressive coefficients of dimension l\times\max{K}. j-th row contains the autoregressive coefficients of regime j.

H

The vector containing the variance weights of the l regimes.

Details

The TAR model is given by

X_t=a_0^{(j)} + \sum_{i=1}^{k_j}a_i^{(j)}X_{t-i}+h^{(j)}e_t

when Z_t\in (r_{j-1},r_j] for som j (j=1,\cdots,l). the \{Z_t\} is the threshold process, l is the number of regimes, k_j is the autoregressive order in the regime j. a_i^{(j)} with i=0,1,\cdots,k_j denote the autoregressive coefficients, while h^{(j)} denote the variance weights. \{e_t\} is the Gaussian white noise process N(0,1).

Value

The time series \{X_t\}.

Author(s)

Hanwen Zhang <hanwenzhang at usantotomas.edu.co>

References

Nieto, F. H. (2005), Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics. Theory and Methods, 34; 905-930

See Also

simu.tar.norm

Examples

set.seed(12345678)
Z<-arima.sim(n=500,list(ar=c(0.5)))
l <- 2
r <- 0
K <- c(2,1)
theta <- matrix(c(1,0.5,-0.3,-0.5,-0.7,NA),nrow=l)
H <- c(1, 1.3)
X <- simu.tar.lognorm(Z,l,r,K,theta,H)
ts.plot(X)