# Param.lognorm: Estimate a TAR model using Gibbs Sampler given the structural... In TAR: Bayesian Modeling of Autoregressive Threshold Time Series Models

## Description

This function estimate a TAR model using Gibbs Sampler given the structural parameters, i.e. the number of regimes, thresholds and autoregressive orders.

## Usage

 1 Param.lognorm(Z, X, l, r, K, n.sim = 500, p.burnin = 0.2, n.thin = 3) 

## Arguments

 Z The threshold series X The series of interest 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. 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 autoregressive coefficients matrix theta and variance weights H. Rows of the matrix theta represent regimes

## 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 15 16 17 18 19 20  # Example 1, TAR model with 2 regimes #' 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) # res <- Param.lognorm(Z,X,l,r,K) # Example 2, TAR model with 3 regimes Z<-arima.sim(n=300, list(ar=c(0.5))) l <- 3 r <- c(-0.6, 0.6) K <- c(1, 2, 1) theta <- matrix(c(1,0.5,-0.5,-0.5,0.2,-0.7,NA, 0.5,NA), nrow=l) H <- c(1, 1.5, 2) X <- simu.tar.lognorm(Z, l, r, K, theta, H) # res <- Param.lognorm(Z,X,l,r,K)