statsmodels.tsa.stattools.range_unit_root_test

statsmodels.tsa.stattools.range_unit_root_test(x, store=False, *, result_object=None)

Range unit-root test for stationarity

Computes the Range Unit-Root (RUR) test for the null hypothesis that x has a unit root, i.e. is not stationary. The null is rejected for small values of the statistic.

Parameters:

xarray_like, 1d

The data series to test.

storebool, optional

If True, then a result instance is returned additionally to the RUR statistic (default is False).

result_objectbool, optional

Flag indicating whether to return the results as a RURResult instead of a plain tuple. The legacy tuple (whose length depends on store) is returned by default and a FutureWarning is issued.

Deprecated since version 0.15.0: In release 0.16.0 or after July 2027, whichever is later, the default will change to always return a RURResult. Set result_object=True to opt in now, or result_object=False to silence the warning and keep the current return type.

Returns:

RURResult

If result_object=True, a result object with fields statistic, pvalue, critical_values, and resstore (resstore is None when not computed). See RURResult.

Otherwise (the deprecated default), a plain tuple whose length depends

on store, made up of a subset of:

statisticfloat

The RUR test statistic.

pvaluefloat

The p-value of the test. The p-value is the smallest probability level in Table 1 of Aparicio et al. (2006) whose critical value is larger than the statistic. The boundary value 0.01 is returned if the statistic is below the 1% critical value, and 0.95 if it is at or above the 95% critical value, that is, if the actual p-value is outside the interval (0.01, 0.95).

critdict

The critical values at 10%, 5%, 2.5% and 1%. Based on Aparicio et al. (2006).

resstore(optional) instance of ResultsStore

An instance of a dummy class with results attached as attributes.

Notes

The critical values are interpolated in the number of observations from Table 1 of Aparicio et al. (2006). The p-value is the smallest tabulated probability level whose critical value is larger than the statistic. If the computed statistic is below the 1% critical value or at or above the 95% critical value, then an InterpolationWarning is issued. In the first case the actual p-value is smaller than the reported 0.01 and in the second it is larger than the reported 0.95.

Changed in version 0.15.1: The null hypothesis is documented correctly: the null is that x has a unit root, and it is rejected for small values of the statistic. The InterpolationWarning previously reported the opposite direction, and was raised when the p-value was 0.95 or 0.01 rather than when the statistic was outside of the tabulated critical values. It is now raised when the statistic is below the 1% critical value (the actual p-value is smaller) or at or above the 95% critical value (the actual p-value is larger).

Missing values are not handled.

References

[1]

Aparicio, F., Escribano A., Sipols, A.E. (2006). Range Unit-Root (RUR) tests: robust against nonlinearities, error distributions, structural breaks and outliers. Journal of Time Series Analysis, 27 (4): 545-576.