# reg.thr.norm: Identify the number of regimes and the corresponding... In TAR: Bayesian Modeling of Autoregressive Threshold Time Series Models

## Description

This function identify the number of regimes and the corresponding thresholds for a TAR model with Gaussian noise process.

## Usage

 1 reg.thr.norm(Z, X, n.sim = 500, p.burnin = 0.2, n.thin = 1) 

## Arguments

 Z The threshold series X The series of interest n.sim Number of iteration for the Gibbs Sampler p.burnin Percentage of iterations used for Burn-in n.thin Thinnin factor for the Gibbs Sampler

## 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 function returns the identified number of regimes with posterior probabilities and the thresholds with credible intervals.

## 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

LS.norm
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 set.seed(12345678) # Example 1, TAR model with 2 regimes Z<-arima.sim(n=300,list(ar=c(0.5))) l <- 2 r <- 0 K <- c(2,1) theta <- matrix(c(1,-0.5,0.5,-0.7,-0.3,NA), nrow=l) H <- c(1, 1.5) X <- simu.tar.norm(Z,l,r,K,theta,H) #res <- reg.thr.norm(Z,X) #res$L.est #res$L.prob #res$R.est #res$R.CI