mTAR: Estimation of a Multivariate Two-Regime SETAR Model

In NTS: Nonlinear Time Series Analysis

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")

Example output

Input error in thrV. Reset to a SETAR model 
Threshold:  0 
Regime 1 with sample size:  572 
Model for the  1 -th component (including constant, if any):  
         est   s.e. t-ratio
[1,] -0.0217 0.0683 -0.3176
[2,]  0.5390 0.0491 10.9782
[3,]  0.2675 0.0279  9.6028
Model for the  2 -th component (including constant, if any):  
         est   s.e. t-ratio
[1,] -0.0038 0.0700 -0.0543
[2,]  0.7016 0.0503 13.9369
[3,]  0.1874 0.0286  6.5628
sigma:  
           [,1]       [,2]
[1,] 0.91518743 0.02272492
[2,] 0.02272492 0.96208513
Information(aic,bix,hq):  -63.13902 -41.39332 -54.65582 
  
Regime 2 with sample size:  427 
Model for the  1 -th component (including constant, if any):  
        est   s.e. t-ratio
[1,] 0.1184 0.0790  1.4992
[2,] 0.3529 0.0618  5.7105
[3,] 0.4563 0.0383 11.9281
Model for the  2 -th component (including constant, if any):  
         est   s.e.  t-ratio
[1,]  0.0326 0.0811   0.4018
[2,]  0.5937 0.0635   9.3533
[3,] -0.5407 0.0393 -13.7592
sigma:  
            [,1]        [,2]
[1,]  0.99425943 -0.05610938
[2,] -0.05610938  1.04933626
Information(aic,bic,hq):  26.81466 47.09858 34.82645 
  
Overall pooled estimate of sigma:  
            [,1]        [,2]
[1,]  0.94898498 -0.01097103
[2,] -0.01097103  0.99937866
Overall information criteria(aic,bic,hq):  -36.32436 5.70526 -19.82937 
Input error in thrV. Reset to a SETAR model 
Estimated Threshold:  -0.02540375 
Regime 1 with sample size:  569 
Model for the  1 -th component (including constant, if any):  
         est   s.e. t-ratio
[1,] -0.0293 0.0688 -0.4257
[2,]  0.5371 0.0493 10.9000
[3,]  0.2636 0.0280  9.4108
Model for the  2 -th component (including constant, if any):  
         est   s.e. t-ratio
[1,] -0.0009 0.0704 -0.0123
[2,]  0.7002 0.0504 13.8930
[3,]  0.1927 0.0287  6.7268
sigma:  
           [,1]       [,2]
[1,] 0.91599927 0.02499769
[2,] 0.02499769 0.95827775
Information(aic,bix,hq):  -64.57853 -42.85913 -56.10362 
  
Regime 2 with sample size:  430 
Model for the  1 -th component (including constant, if any):  
        est   s.e. t-ratio
[1,] 0.1211 0.0780  1.5522
[2,] 0.3509 0.0612  5.7307
[3,] 0.4586 0.0378 12.1344
Model for the  2 -th component (including constant, if any):  
         est   s.e.  t-ratio
[1,]  0.0437 0.0803   0.5436
[2,]  0.5864 0.0630   9.3031
[3,] -0.5363 0.0389 -13.7849
sigma:  
            [,1]        [,2]
[1,]  0.98909600 -0.05273914
[2,] -0.05273914  1.04810883
Information(aic,bic,hq):  24.33488 44.65381 32.35822 
  
Overall pooled estimate of sigma:  
             [,1]         [,2]
[1,]  0.947462326 -0.008462609
[2,] -0.008462609  0.996943783
Overall information criteria(aic,bic,hq):  -40.24365 1.794681 -23.7454 

NTS documentation built on Aug. 6, 2020, 5:08 p.m.