# arch.unitroot.VarianceRatio¶

class arch.unitroot.VarianceRatio(y, lags=2, trend='c', debiased=True, robust=True, overlap=True)[source]

Variance Ratio test of a random walk.

Parameters
• y ({ndarray, Series}) – The data to test for a random walk

• lags (int) – The number of periods to used in the multi-period variance, which is the numerator of the test statistic. Must be at least 2

• trend ({"n", "c"}, optional) – “c” allows for a non-zero drift in the random walk, while “n” requires that the increments to y are mean 0

• overlap (bool, optional) – Indicates whether to use all overlapping blocks. Default is True. If False, the number of observations in y minus 1 must be an exact multiple of lags. If this condition is not satisfied, some values at the end of y will be discarded.

• robust (bool, optional) – Indicates whether to use heteroskedasticity robust inference. Default is True.

• debiased (bool, optional) – Indicates whether to use a debiased version of the test. Default is True. Only applicable if overlap is True.

Notes

The null hypothesis of a VR is that the process is a random walk, possibly plus drift. Rejection of the null with a positive test statistic indicates the presence of positive serial correlation in the time series.

Examples

>>> from arch.unitroot import VarianceRatio
>>> import datetime as dt
>>> data = pdr.get_data_fred("DJIA")
>>> data = data.resample("M").last()  # End of month
>>> returns = data["DJIA"].pct_change().dropna()
>>> vr = VarianceRatio(returns, lags=12)
>>> print("{0:0.4f}".format(vr.pvalue))
0.0000


References

*

Campbell, John Y., Lo, Andrew W. and MacKinlay, A. Craig. (1997) The Econometrics of Financial Markets. Princeton, NJ: Princeton University Press.

Methods

 Summary of test, containing statistic, p-value and critical values

Properties

 alternative_hypothesis The alternative hypothesis critical_values Dictionary containing critical values specific to the test, number of observations and included deterministic trend terms. debiased Sets of gets the indicator to use debiased variances in the ratio lags Sets or gets the number of lags used in the model. nobs The number of observations used when computing the test statistic. null_hypothesis The null hypothesis overlap Sets of gets the indicator to use overlapping returns in the long-period variance estimator pvalue Returns the p-value for the test statistic robust Sets of gets the indicator to use a heteroskedasticity robust variance estimator stat The test statistic for a unit root trend Sets or gets the deterministic trend term used in the test. valid_trends List of valid trend terms. vr The ratio of the long block lags-period variance to the 1-period variance y Returns the data used in the test statistic