mTAR: Estimation of a Multivariate Two-Regime SETAR Model

In NTS: Nonlinear Time Series Analysis

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.