# 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```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.