# uTAR: Estimation of a Univariate Two-Regime SETAR Model In NTS: Nonlinear Time Series Analysis

## 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

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

## 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.

## 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.

## 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``` ```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) ```

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