# simu.tar.lognorm: Simulate a series from a log-normal TAR model with Gaussian... In TAR: Bayesian Modeling of Autoregressive Threshold Time Series Models

## 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

 1 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)} + ∑_{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

simu.tar.norm
 1 2 3 4 5 6 7 8 9 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)