Description Usage Arguments Details Value Author(s) References See Also Examples

Estimation of a two-regime TAR model.

1 2 3 |

`y` |
time series |

`p1` |
AR order of the lower regime |

`p2` |
AR order of the upper regime |

`d` |
delay parameter |

`is.constant1` |
if True, intercept included in the lower regime, otherwise the intercept is fixed at zero |

`is.constant2` |
similar to is.constant1 but for the upper regime |

`transform` |
available transformations: "no" (i.e. use raw data), "log", "log10" and "sqrt" |

`center` |
if set to be True, data are centered before analysis |

`standard` |
if set to be True, data are standardized before analysis |

`estimate.thd` |
if True, threshold parameter is estimated, otherwise it is fixed at the value supplied by threshold |

`threshold` |
known threshold value, only needed to be supplied if estimate.thd is set to be False. |

`method` |
"MAIC": estimate the TAR model by minimizing the AIC; "CLS": estimate the TAR model by the method of Conditional Least Squares. |

`a` |
lower percent; the threshold is searched over the interval defined by the a*100 percentile to the b*100 percentile of the time-series variable |

`b` |
upper percent |

`order.select` |
If method is "MAIC", setting order.select to True will enable the function to further select the AR order in each regime by minimizing AIC |

`print` |
if True, the estimated model will be printed |

The two-regime Threshold Autoregressive (TAR) model is given by the following formula:

*
Y_t = φ_{1,0}+φ_{1,1} Y_{t-1} +…+ φ_{1,p} Y_{t-p_1} +σ_1 e_t,
\mbox{ if } Y_{t-d}≤ r *

* Y_t = φ_{2,0}+φ_{2,1} Y_{t-1} +…+φ_{2,p_2} Y_{t-p}+σ_2 e_t,
\mbox{ if } Y_{t-d} > r.*

where r is the threshold and d the delay.

A list of class "TAR" which can be further processed by the by the predict and tsdiag functions.

Kung-Sik Chan

Tong, H. (1990) "Non-linear Time Series, a Dynamical System Approach," Clarendon Press Oxford

"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan

`predict.TAR`

,
`tsdiag.TAR`

,
`tar.sim`

,
`tar.skeleton`

1 2 |

```
Attaching package: 'TSA'
The following objects are masked from 'package:stats':
acf, arima
The following object is masked from 'package:utils':
tar
time series included in this analysis is: log(prey.eq)
SETAR(2, 1 , 4 ) model delay = 3
estimated threshold = 4.661 from a Minimum AIC fit with thresholds
searched from the 17 percentile to the 81 percentile of all data.
The estimated threshold is the 56.6 percentile of
all data.
lower regime:
Residual Standard Error=0.2341
R-Square=0.9978
F-statistic (df=2, 28)=6355.76
p-value=0
Estimate Std.Err t-value Pr(>|t|)
intercept-log(prey.eq) 0.2621 0.3156 0.8305 0.4133
lag1-log(prey.eq) 1.0175 0.0704 14.4455 0.0000
(unbiased) RMS
0.05479
with no of data falling in the regime being
log(prey.eq) 30
(max. likelihood) RMS for each series (denominator=sample size in the regime)
log(prey.eq) 0.05114
upper regime:
Residual Standard Error=0.2676
R-Square=0.9971
F-statistic (df=5, 18)=1253.556
p-value=0
Estimate Std.Err t-value Pr(>|t|)
intercept-log(prey.eq) 4.1986 1.2841 3.2697 0.0043
lag1-log(prey.eq) 0.7081 0.2023 3.5005 0.0026
lag2-log(prey.eq) -0.3009 0.3118 -0.9648 0.3474
lag3-log(prey.eq) 0.2788 0.4063 0.6861 0.5014
lag4-log(prey.eq) -0.6113 0.2726 -2.2427 0.0377
(unbiased) RMS
0.07158
with no of data falling in the regime being
23
(max. likelihood) RMS for each series (denominator=sample size in the regime)
0.05602
Nominal AIC is 10.92
```

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