# arch.unitroot.DFGLS¶

class arch.unitroot.DFGLS(y, lags=None, trend='c', max_lags=None, method='AIC', low_memory=None)[source]

Elliott, Rothenberg and Stock’s GLS version of the Dickey-Fuller test

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

• lags (int, optional) – The number of lags to use in the ADF regression. If omitted or None, method is used to automatically select the lag length with no more than max_lags are included.

• trend ({"c", "ct"}, optional) –

The trend component to include in the test

• ”c” - Include a constant (Default)

• ”ct” - Include a constant and linear time trend

• max_lags (int, optional) – The maximum number of lags to use when selecting lag length

• method ({"AIC", "BIC", "t-stat"}, optional) –

The method to use when selecting the lag length

• ”AIC” - Select the minimum of the Akaike IC

• ”BIC” - Select the minimum of the Schwarz/Bayesian IC

• ”t-stat” - Select the minimum of the Schwarz/Bayesian IC

Notes

The null hypothesis of the Dickey-Fuller GLS is that there is a unit root, with the alternative that there is no unit root. If the pvalue is above a critical size, then the null cannot be rejected and the series appears to be a unit root.

DFGLS differs from the ADF test in that an initial GLS detrending step is used before a trend-less ADF regression is run.

Critical values and p-values when trend is “c” are identical to the ADF. When trend is set to “ct”, they are from …

Examples

>>> from arch.unitroot import DFGLS
>>> import numpy as np
>>> import statsmodels.api as sm
>>> inflation = np.diff(np.log(data["cpi"]))
>>> dfgls = DFGLS(inflation)
>>> print("{0:0.4f}".format(dfgls.stat))
-2.7611
>>> print("{0:0.4f}".format(dfgls.pvalue))
0.0059
>>> dfgls.lags
2
>>> dfgls.trend = "ct"
>>> print("{0:0.4f}".format(dfgls.stat))
-2.9036
>>> print("{0:0.4f}".format(dfgls.pvalue))
0.0447


References

*

Elliott, G. R., T. J. Rothenberg, and J. H. Stock. 1996. Efficient bootstrap for an autoregressive unit root. Econometrica 64: 813-836

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. lags Sets or gets the number of lags used in the model. max_lags Sets or gets the maximum lags used when automatically selecting lag length nobs The number of observations used when computing the test statistic. null_hypothesis The null hypothesis pvalue Returns the p-value for the test statistic regression Returns the OLS regression results from the ADF model estimated 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. y Returns the data used in the test statistic