uTAR | R Documentation |

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.

```
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
)
```

`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. |

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. |

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

```
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)
```

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