ARorder.norm {TAR}

Identify the autoregressive orders for a Gaussian TAR model given the number of regimes and thresholds.

Description

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

Usage

ARorder.norm(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

n.thin

Thinnin factor for the Gibbs Sampler

Details

The TAR model is given by

X_t=a_0^{(j)} + \sum_{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 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

See Also

simu.tar.norm

Examples

set.seed(123456789)
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 <- ARorder.norm(Z,X,l,r)
#res$K.est
#res$K.prob