# LS.norm: Estimate a Gaussian TAR model using Least Square method given... In TAR: Bayesian Modeling of Autoregressive Threshold Time Series Models

## Description

This function estimate a Gaussian TAR model using Least Square method given the structural parameters, i.e. the number of regimes, thresholds and autoregressive orders.

## Usage

 1 LS.norm(Z, X, l, r, K) 

## 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.

## 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.

## 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

simu.tar.norm

## Examples

 1 2 3 4 5 6 7 8 Z<-arima.sim(n=500,list(ar=c(0.5))) l <- 2 r <- 0 K <- c(2,1) theta <- matrix(c(1,-0.5,0.5,-0.7,-0.3,NA), nrow=l) H <- c(1, 1.5) X <- simu.tar.norm(Z,l,r,K,theta,H) LS.norm(Z,X,l,r,c(0,0)) 

### Example output

Loading required package: mvtnorm
$theta.est [,1] [1,] 1.1860249 [2,] -0.6094069$h.est
[1] 1.485759 1.996804


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