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

This function performs a ratio-based test against a change in persistence. 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.

1 2 3 | ```
ratio_test(x, trend = c("none", "linear"), tau = 0.2,
statistic = c("mean", "max", "exp"), type = c("BT", "LT", "HLT",
"HLTmin"), m = 0, z = 9, simu = 0, M = 10000)
``` |

`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, |

`type` |
which type of ratio test should be performed, |

`m` |
Number of covariances used for the estimation of the long run variance if |

`z` |
Number of polynomials used if |

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

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

Busetti and Taylor (2004) (BT) introduced a test that is able to identify when time series exhibit changes in persistence. Under the null hypothesis, the series is constant I(0), i.e. stationary. Under the alternative the series exhibits a break either from I(0) to I(1) or I(1) to I(0). As the test is oversized for weakly dependent time series, Leybourne and Taylor (2004) (LT) standardized the test statistic by an estimate of the long run variance using m lags. Another problem is that constant I(1) processes are neither covered under the null nor the alternative. Here, the test often rejects the null although no change in persistence occured. Harvey, Leybourne, and Taylor (2006) (HLT) introduced a modification where they multiply the test statistic by a unit root test. This allows the test statistic to have the same critical values under both constant I(0) and constant I(1). It should be noted, however, that only the critical values are identical, the distribution is highly irregular.

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 Harvey, Leybourne, and Taylor (2006). These are, however, only valid for `tau=0.2`

, `m=0`

, and `z=9`

.
In case that non-default values are chosen for `tau`

, `m`

, or `z`

, it is recommended to set `simu=1`

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

and `M=10,000`

replications this takes approximately fifteen 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.

Leybourne, S. and Taylor, R. (2004): On tests for changes in persistence. Economics letters, 84, pp. 107-115.

Harvey, D., Leybourne, S. and Taylor, R. (2006): Modified tests for a change in persistence. Journal of Econometrics, 134, pp. 441-469.

`cusum_test`

, `LBI_test`

, `LKSN_test`

, `MR_test`

.

1 2 3 4 5 6 7 |

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