ARorder.lognorm {TAR}

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

Description

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

Usage

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)} + \sum_{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

See Also

simu.tar.lognorm, ARorder.norm

Examples

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