BAYSTAR {BAYSTAR}R Documentation

Threshold Autoregressive model: Bayesian approach

Description

Bayesian estimation and inference for two-regime TAR model, as well as monitoring MCMC convergence. One may want to allow for higher-order AR models in the different regimes. Parsimonious subset AR could be assigned in each regime in the BAYSTAR function rather than a full AR model (i.e. Autoregressive order could be not a continuous series).

Usage

BAYSTAR(x, lagp1, lagp2, nIteration, nBurnin, constant = 1, differ = 0, d0 = 3, step.thv)

BAYSTAR(x, lagp1, lagp2, nIteration, nBurnin, constant = 1, differ = 0, d0 = 3, step.thv, thresVar)

Arguments

x Time series.
lagp1 The vector of non-zero autoregressive lags for the lower regime. (regime one); e.g. An AR model with p1=3, it could be non-zero lags 1,3, and 5 would set lagp1<-c(1,3,5).
lagp2 The vector of non-zero autoregressive lags for the upper regime. (regime two)
nIteration Total MCMC iterations.
nBurnin Burn-in iterations.
constant Use the CONSTANT option to fit a model with/without a constant term (1/0). By default CONSTANT=1.
differ Take the first difference. (default = 0)
d0 The option of a set maximum delay. (default = 3)
step.thv Step size of threshold variable for the MH algorithm are controlled the proposal variance.
thresVar Exogenous threshold variable. (if missing, the series x is used.)

Details

Given the maximum AR orders p1 and p2, the two-regime SETAR(2:p1;p2) model is specified as:

x_{t} = ( phi _0^{(1)} + phi _1^{(1)} x_{t - 1} + ... + phi _{p_1 }^{(1)} x_{t - p_1 } + a_t^{(1)} ) I( z_{t-d} <= th) + ( phi _0^{(2)} + phi _1^{(2)} x_{t - 1} + ... + phi _{p_2 }^{(2)} x_{t - p_2 } + a_t^{(2)} I( z_{t-d} > th)

where th is the threshold parameter driving the regime-switching behavior; z_{t} is the threshold variable; d is the threshold lag of the model; and the error term a_t^{(j)} in regime j, (j=1,2) is assumed to be an i.i.d. Gaussian white noise process with mean zero and variance sigma_j^2, j=1,2. I[A] is an indicator function with I[A]=1 if the event A occurs and I[A]=0 otherwise. One may want to allow parsimonious subset AR model in each regime rather than a full AR model.

Value

A list with output containing the following components:

mcmc the mcmc results of all parameters (including burn-in).
coef summarize the collected MCMC estimates after burn-in. Including all parameters of TAR model.
residual the residuals from the fitting model by coef.
lagd The mode of time delay of threshold variable in MCMC iteration.

Author(s)

Cathy W. S. Chen, Edward M.H. Lin, F.C. Liu, and Richard Gerlach

Examples

data(unemployrate)
x<- unemployrate
lagp1<-c(2,3,4,10,12)
lagp2<-c(2,3,12)
## Total MCMC iterations and burn-in iterations
nIterations<- 10000
nBurnin<- 2000
## Step size for the MH algorithm
step.thv<- 2.0
y<-BAYSTAR(x,lagp1,lagp2,nIterations,nBurnin,constant=0,differ=1,d0=3,step.thv=step.thv)

[Package BAYSTAR version 0.1-2 Index]