nonlintest | R Documentation |

A bootstrap test of non-linearity in a time series using the third-order moment.

nonlintest(data, n.lag, n.boot, alpha = 0.05)

`data` |
a vector of equally spaced numeric observations (time series). |

`n.lag` |
the number of lags tested using the third-order moment, maximum = length of time series. |

`n.boot` |
the number of bootstrap replications (suggested minimum of 100; 1000 or more would be better). |

`alpha` |
statistical significance level of test (default=0.05). |

The test uses `aaft`

to create linear surrogates with the same
second-order properties, but no (third-order) non-linearity. The third-order
moments (`third`

) of these linear surrogates and the actual series are
then compared from lags 0 up to `n.lag`

(excluding the skew at the
co-ordinates (0,0)). The bootstrap test works on the overall area outside
the limits, and gives an indication of the overall non-linearity. The plot
using `region`

shows those co-ordinates of the third order moment that
exceed the null hypothesis limits, and can be a useful clue for guessing the
type of non-linearity. For example, a large value at the co-ordinates (0,1)
might be caused by a bi-linear series *X_t=α
X_{t-1}\varepsilon_{t-1} +\varepsilon_t*.

Returns an object of class “nonlintest” with the following parts:

`region` |
the region of the third order moment where the test
exceeds the limits (up to |

`n.lag` |
the maximum lag tested using the third-order moment. |

`stats` |
a list of following statistics for the area outside the test limits: |

`outside` |
the total area outside of limits (summed over the whole third-order moment). |

`stan` |
the total area outside the limits divided by its standard deviation to give a standardised estimate. |

`median` |
the median area outside the test limits. |

`upper` |
the (1- |

`pvalue` |
Bootstrap p-value of the area outside the limits to test if the series is linear. |

`test` |
Reject the null hypothesis that the series is linear (TRUE/FALSE). |

Adrian Barnett a.barnett@qut.edu.au

Barnett AG & Wolff RC (2005) A Time-Domain Test for Some Types
of Nonlinearity, *IEEE Transactions on Signal Processing*, vol 53,
pages 26–33

`print.nonlintest`

, `plot.nonlintest`

data(CVD) ## Not run: test.res = nonlintest(data=CVD$cvd, n.lag=4, n.boot=1000)

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.