arch.unitroot.VarianceRatio¶

class arch.unitroot.VarianceRatio(y: ndarray | DataFrame | Series, lags: int = 2, trend: 'n' | 'c' = 'c', debiased: bool = True, robust: bool = True, overlap: bool = True)[source]¶

Variance Ratio test of a random walk.

Parameters:¶

y: ndarray | DataFrame | Series¶: The data to test for a random walk
lags: int = 2¶: 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' = 'c'¶: “c” allows for a non-zero drift in the random walk, while “n” requires that the increments to y are mean 0
overlap: bool = True¶: 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 = True¶: Indicates whether to use heteroskedasticity robust inference. Default is True.
debiased: bool = True¶: 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. See [1] for details about variance ratio testing.

Examples

>>> from arch.unitroot import VarianceRatio
>>> import pandas_datareader as pdr
>>> data = pdr.get_data_fred("DJIA", start="2010-1-1", end="2020-12-31")
>>> data = np.log(data.resample("M").last())  # End of month
>>> vr = VarianceRatio(data, lags=12)
>>> print(f"{vr.pvalue:0.4f}")
0.1370

References

Methods

`summary`()	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