# ARorder.lognorm: Identify the autoregressive orders for a log-normal TAR model... In TAR: Bayesian Modeling of Autoregressive Threshold Time Series Models

## Description

This function identify the autoregressive orders for a log-normal TAR model given the number of regimes and thresholds.

## Usage

 1 2 ARorder.lognorm(Z, X, l, r, k_Max = 3, k_Min = 0, n.sim = 500, p.burnin = 0.3, n.thin = 1) 

## 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_Max The minimum value for each autoregressive order. The default is 3. k_Min The maximum value for each autoregressive order. The default is 0. 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 log-normal TAR model is given by

log X_t=a_0^{(j)} + ∑_{i=1}^{k_j}a_i^{(j)}log X_{t-i}+h^{(j)}e_t

when Z_t\in (r_{j-1},r_j] for some 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 identified autoregressive orders with posterior probabilities

## 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.lognorm, ARorder.norm

## Examples

  1 2 3 4 5 6 7 8 9 10 11 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 <- ARorder.lognorm(Z,X,l,r) #res$K.est #res$K.prob 

### Example output

Loading required package: mvtnorm


TAR documentation built on May 2, 2019, 3:40 a.m.