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 ({'nc', 'c'}, optional) -- 'c' allows for a non-zero drift in the random walk, while 'nc' 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
>>> import pandas_datareader as pdr
>>> 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()

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