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

This function performs the locally best invariant test against a change in persistence as suggested by Busetti and Taylor (2004). Under the null hypothesis the time series is I(0) throughout and under the alternative a change from either I(1) to I(0) or I(0) to I(1) has occured.

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`x` |
the univariate numeric vector to be investigated. Missing values are not allowed. |

`trend` |
whether the time series exhibits a trend, |

`tau` |
the function tests in the interval |

`statistic` |
which type of test statistic should be used, |

`simu` |
whether critical values should be simulated or interpolated, |

`M` |
number of replications in case critical values should be simulated. Default is |

The critical values of the tests vary with the sample size. If `simu=0`

, the critical values provided
are based on linear interpolation of the critical values simulated by Busetti and Taylor (2004). These are, however, only valid for `tau=0.2`

.
In case that another value is chosen for `tau`

, it is recommended to set `simu=1`

which means that critical values are simulated based on the given data using M replications.
For a time series of length `T=100`

and `M=10,000`

replications this takes approximately five minutes with increasing duration for higher T or M.
It should be noted, however, that M smaller than 10,000 make the results unreliable.

Returns a matrix that consists of test statistic and critical values (corresponding to `alpha=0.1,0.05,0.01`

) for testing against a change from I(1) to I(0), I(0) to I(1), and against a change in an unknown direction.

Janis Becker

Busetti, F. and Taylor, R. (2004): Tests of stationarity against a change in persistence. Journal of Econometrics, 123, pp. 33-66.

`cusum_test`

, `LKSN_test`

, `MR_test`

, `ratio_test`

.

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