NTS (version 1.1.3)

mTAR: 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"
)

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.

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)).

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")