BAYSTAR {BAYSTAR} | R Documentation |
Bayesian estimation and one-step-ahead forecasting 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. the autoregressive orders could be not a continuous series).
BAYSTAR(x, lagp1, lagp2, Iteration, Burnin, constant, d0, step.thv, thresVar, mu01, v01, mu02, v02, v0, lambda0, refresh)
x |
A vector of time series. |
lagp1 |
A vector of non-zero autoregressive lags for the lower regime (regime one).
For example, an AR model with p1=3 in lags 1,3, and 5 would be set
as lagp1<-c(1,3,5) . |
lagp2 |
A vector of non-zero autoregressive lags for the upper regime (regime two). |
Iteration |
The number of MCMC iterations. |
Burnin |
The number of burn-in iterations for the sampler. |
constant |
The intercepts include in the model for each regime, if constant =1.
Otherwise, if constant =0. (Default: constant =1) |
d0 |
The maximum delay lag considered. (Default: d0 = 3) |
step.thv |
Step size of tuning parameter for the Metropolis-Hasting algorithm. |
thresVar |
A vector of time series for the threshold variable. (if missing, the series x is used.) |
mu01 |
The prior mean of phi in regime one. This setting can be a scalar or a column vector with dimension equal to the number of phi. If this sets a scalar value, then the prior mean for all of phi are this value. (Default: a vector of zeros) |
v01 |
The prior covariance matrix of phi in regime one. This setting can either be a scalar or a square matrix with dimensions equal to the number of phi. If this sets a scalar value, then prior covariance matrix of phi is that value times an identity matrix. (Default: a diagonal matrix are set to 0.1) |
mu02 |
The prior mean of phi in regime two. This setting can be a scalar or a column vector with dimension equal to the number of phi. If this sets a scalar value, then the prior mean for all of phi are this value. (Default: a vector of zeros) |
v02 |
The prior covariance matrix of phi in regime two. This setting can either be a scalar or a square matrix with dimensions equal to the number of phi. If this sets a scalar value, then prior covariance matrix of phi is that value times an identity matrix. (Default: a diagonal matrix are set to 0.1) |
v0 |
v0 /2 is the shape parameter for Inverse-Gamma prior of sigma^2.
(Default: v0 = 3) |
lambda0 |
lambda0 *v0 /2 is the scale parameter for Inverse-Gamma prior of
sigma^2. (Default: lambda0 = the residual
mean squared error of fitting an AR(p1) model to the data.) |
refresh |
Each refresh iteration for monitoring MCMC output. (Default: refresh =1000) |
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 _{p1 }^{(1)} x_{t - p1 } + a_t^{(1)} ) I( z_{t-d} <= th) + ( phi _0^{(2)} + phi _1^{(2)} x_{t - 1} + ... + phi _{p2 }^{(2)} x_{t - p2 } + a_t^{(2)} I( z_{t-d} > th)
where th is the threshold value for regime switching; z_{t} is the threshold variable; d is the delay lag of threshold variable; and the error term a_t^{(j)}, j, (j=1,2), for each regime 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. Event A will occur if I(A)=1 and otherwise if I(A)=0. One may want to allow parsimonious subset AR model in each regime rather than a full AR model.
A list of output with containing the following components:
mcmc |
All MCMC iterations. |
posterior |
The initial Burnin iterations are discarded as a burn-in sample, the final sample of (Iteration-Burnin ) iterates is used for posterior inference. |
coef |
Summary Statistics of parameter estimation based on the final sample of (Iteration-Burnin ) iterates. |
residual |
Residuals from the estimated model. |
lagd |
The mode of time delay lag of the threshold variable. |
DIC |
The deviance information criterion (DIC); a Bayesian method for model comparison (Spiegelhalter et al, 2002) |
Cathy W. S. Chen, Edward M.H. Lin, F.C. Liu, and Richard Gerlach
library(BAYSTAR) data(unemployrate) x<- unemployrate nx<- length(x) differ.x<- x[2:nx]-x[2:nx-1] lagp1<- c(2,3,4,10,12) lagp2<- c(2,3,12) ## Total MCMC iterations and burn-in iterations Iteration<- 10000 Burnin<- 2000 ## A RW (random walk) MH algorithm is used in simulating the threshold value ## Step size for the RW MH step.thv<- 2.5 out1 <- BAYSTAR(differ.x,lagp1,lagp2,Iteration,Burnin,constant=0,step.thv=step.thv) d0 <- 4 out2 <- BAYSTAR(differ.x,lagp1,lagp2,Iteration,Burnin,d0,constant=0,step.thv=step.thv) ## Comparison with DIC library(coda) geweke.diag(out2$posterior, frac1=0.1, frac2=0.5)