mTAR: Estimation of a Multivariate Two-Regime SETAR Model In NTS: Nonlinear Time Series Analysis

 mTAR R Documentation

Estimation of a Multivariate Two-Regime SETAR Model

Description

Estimation of a multivariate two-regime SETAR model, including threshold. The procedure of Li and Tong (2016) is used to search for the threshold.

Usage

``````mTAR(
y,
p1,
p2,
thr = NULL,
thrV = NULL,
delay = c(1, 1),
Trim = c(0.1, 0.9),
k0 = 300,
include.mean = TRUE,
score = "AIC"
)
``````

Arguments

 `y` a (`nT`-by-`k`) data matrix of multivariate time series, where `nT` is the sample size and `k` is the dimension. `p1` AR-order of regime 1. `p2` AR-order of regime 2. `thr` threshold variable. Estimation is needed if `thr` = NULL. `thrV` vector of threshold variable. If it is not null, thrV must have the same sample size of that of y. `delay` two elements (i,d) with "i" being the component and "d" the delay for threshold variable. `Trim` lower and upper quantiles for possible threshold value. `k0` the maximum number of threshold values to be evaluated. `include.mean` logical values indicating whether constant terms are included. `score` the choice of criterion used in selection threshold, namely (AIC, det(RSS)).

Value

mTAR returns a list with the following components:

 `data` the data matrix, y. `beta` a (`p*k+1`)-by-(`2k`) matrices. The first `k` columns show the estimation results in regime 1, and the second `k` columns show these in regime 2. `arorder` AR orders of regimes 1 and 2. `sigma` estimated innovational covariance matrices of regimes 1 and 2. `residuals` estimated innovations. `nobs` numbers of observations in regimes 1 and 2. `model1, model2` estimated models of regimes 1 and 2. `thr` threshold value. `delay` two elements (`i`,`d`) with "`i`" being the component and "`d`" the delay for threshold variable. `thrV` vector of threshold variable. `D` a set of positive threshold values. `RSS` residual sum of squares. `information` overall information criteria. `cnst` logical values indicating whether the constant terms are included in regimes 1 and 2. `sresi` standardized residuals.

References

Li, D., and Tong. H. (2016) Nested sub-sample search algorithm for estimation of threshold models. Statisitca Sinica, 1543-1554.

Examples

``````phi1=matrix(c(0.5,0.7,0.3,0.2),2,2)
phi2=matrix(c(0.4,0.6,0.5,-0.5),2,2)
sigma1=matrix(c(1,0,0,1),2,2)
sigma2=matrix(c(1,0,0,1),2,2)
c1=c(0,0)
c2=c(0,0)
delay=c(1,1)
Trim=c(0.2,0.8)
include.mean=TRUE
y=mTAR.sim(1000,0,phi1,phi2,sigma1,sigma2,c1,c2,delay,ini=500)
est=mTAR(y\$series,1,1,0,y\$series,delay,Trim,300,include.mean,"AIC")
est2=mTAR(y\$series,1,1,NULL,y\$series,delay,Trim,300,include.mean,"AIC")
``````

NTS documentation built on Sept. 25, 2023, 1:08 a.m.