# Likelihood ratio test for threshold nonlinearity

### Description

Carry out the likelihood ratio test for threshold nonlinearity, with the null hypothesis being a normal AR process and the alternative hypothesis being a TAR model with homogeneous, normally distributed errors.

### Usage

1 |

### Arguments

`y` |
time series |

`p` |
working AR order |

`d` |
delay |

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

`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 |

`...` |
other arguments to be passed to the ar function which determines the Ar order, if p is missing |

### Details

The search for the threshold parameter may be narrower than that defined by the user as the function attempts to ensure adequate sample size in each regime of the TAR model. The p-value of the test is based on large-sample approximation and also is more reliable for small p-values.

### Value

`p.value` |
p-value of the test |

`test.statistic` |
likelihood ratio test statistic |

`a` |
the actual lower fraction that defines the interval of search for the threshold; it may differ from the a specified by the user |

`b` |
the actual upper fraction that defines the interval of search for the threshold |

### Author(s)

Kung-Sik Chan

### References

Chan, K.S. (1990). Percentage points of likelihood ratio tests for threshold autoregression. Journal of Royal Statistical Society, B 53, 3, 691-696.

### See Also

`Keenan.test`

, `Tsay.test`

### Examples

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