Description Usage Arguments Details Author(s) References Examples

Test for seasonal unit root roots in a time series.

1 2 |

`x` |
time series |

`method` |
"OLS" or "ML" |

`augmentations` |
non-seasonal and seasonal order of the augmentations |

`freq` |
frequency to be tested |

`nrun` |
number of runs in monte carlo simulation |

`seed` |
seed for monte carlo simulated based generation of null distribution |

The null hypothesis of the OCSB is that a series contains a seasonal unit root. This is tested by a Dickey-Fuller type regression. The test regression has often to be augmented by autocorrelational terms to ensure white noise of the error terms.

If seasonal lags are included and method='OLS' the test regression is calculated by OLS, so only the seasonal lags are included. If instead of 'OLS' method='ML' a seasonal AR model is calculated, which implies that high-order non-seasonal lags will be indirectly included as well (see Box and Jenkins, 1970). For seasonal augmentations, ML is quite a bit slower than OLS. The run time can be speeded up by reducing the number of runs of the monte carlo simulation (e.g. nrun=100).

Under the null hypothesis the test statistic follows a non-standard distribution and thus needs to be simulated. The number of runs and the seed can be changed.

Daniel Ollech

Box, G. and G. Jenkins (1970). Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day.

Osborn D.R., Chui A.P.L., Smith J., and Birchenhall C.R. (1988). Seasonality and the order of integration for consumption, Oxford Bulletin of Economics and Statistics 50(4):361-377.

1 2 | ```
teststat <- ocsb(ts(rnorm(70, 10,10), frequency=7), nrun=200)
check_residuals(teststat)
``` |

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