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

lagsint, 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_lagsint, 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 …

References

*

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

Examples

>>> from arch.unitroot import DFGLS
>>> import numpy as np
>>> import statsmodels.api as sm
>>> data = sm.datasets.macrodata.load().data
>>> 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
Attributes
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

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

Methods

summary()

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

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.

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