NTS (version 1.1.3)

uTAR: Estimation of a Univariate Two-Regime SETAR Model

Description

Estimation of a univariate two-regime SETAR model, including threshold value, performing recursive least squares method or nested sub-sample search algorithm. The procedure of Li and Tong (2016) is used to search for the threshold.

Usage

uTAR(
  y,
  p1,
  p2,
  d = 1,
  thrV = NULL,
  thrQ = c(0, 1),
  Trim = c(0.1, 0.9),
  include.mean = TRUE,
  method = "RLS",
  k0 = 300
)

Value

uTAR returns a list with components:

data

the data matrix, y.

arorder

AR orders of regimes 1 and 2.

delay

the delay for threshold variable.

residuals

estimated innovations.

sresi

standardized residuals.

coef

a 2-by-(p+1) matrices. The first row shows the estimation results in regime 1, and the second row shows these in regime 2.

sigma

estimated innovational covariance matrices of regimes 1 and 2.

nobs

numbers of observations in regimes 1 and 2.

model1,model2

estimated models of regimes 1 and 2.

thr

threshold value.

D

a set of threshold values.

RSS

RSS

AIC

AIC value

cnst

logical values indicating whether the constant terms are included in regimes 1 and 2.

Arguments

y

a vector of time series.

p1, p2

AR-orders of regime 1 and regime 2.

d

delay for threshold variable, default is 1.

thrV

threshold variable. If thrV is not null, it must have the same length as that of y.

thrQ

lower and upper quantiles to search for threshold value.

Trim

lower and upper quantiles for possible threshold values.

include.mean

a logical value indicating whether constant terms are included.

method

"RLS": estimate the model by conditional least squares method implemented by recursive least squares; "NeSS": estimate the model by conditional least squares method implemented by Nested sub-sample search (NeSS) algorithm.

k0

the maximum number of threshold values to be evaluated, when the nested sub-sample search (NeSS) method is used. If the sample size is large (> 3000), then k0 = floor(nT*0.5). The default is k0=300. But k0 = floor(nT*0.8) if nT < 300.

References

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

Examples

phi=t(matrix(c(-0.3, 0.5,0.6,-0.3),2,2))
y=uTAR.sim(nob=2000, arorder=c(2,2), phi=phi, d=2, thr=0.2, cnst=c(1,-1),sigma=c(1, 1))$series
est=uTAR(y=y,p1=2,p2=2,d=2,thrQ=c(0,1),Trim=c(0.1,0.9),include.mean=TRUE,method="NeSS",k0=50)