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scikits.statsmodels.tsa.stattools.adfuller

scikits.statsmodels.tsa.stattools.adfuller(x, maxlag=None, regression='c', autolag='AIC', store=False, regresults=False)[source]

Augmented Dickey-Fuller unit root test

The Augmented Dickey-Fuller test can be used to test for a unit root in a univariate process in the presence of serial correlation.

Parameters :

x : array_like, 1d

data series

maxlag : int

Maximum lag which is included in test, default 12*(nobs/100)^{1/4}

regression : str {‘c’,’ct’,’ctt’,’nc’}

Constant and trend order to include in regression * ‘c’ : constant only * ‘ct’ : constant and trend * ‘ctt’ : constant, and linear and quadratic trend * ‘nc’ : no constant, no trend

autolag : {‘AIC’, ‘BIC’, ‘t-stat’, None}

  • if None, then maxlag lags are used
  • if ‘AIC’ or ‘BIC’, then the number of lags is chosen to minimize the corresponding information criterium
  • ‘t-stat’ based choice of maxlag. Starts with maxlag and drops a lag until the t-statistic on the last lag length is significant at the 95 % level.

store : bool

If True, then a result instance is returned additionally to the adf statistic

regresults : bool

If True, the full regression results are returned.

Returns :

adf : float

Test statistic

pvalue : float

MacKinnon’s approximate p-value based on MacKinnon (1994)

usedlag : int

Number of lags used.

nobs : int

Number of observations used for the ADF regression and calculation of the critical values.

critical values : dict

Critical values for the test statistic at the 1 %, 5 %, and 10 % levels. Based on MacKinnon (2010)

icbest : float

The maximized information criterion if autolag is not None.

regresults : RegressionResults instance

The

resstore : (optional) instance of ResultStore

an instance of a dummy class with results attached as attributes

Notes

The null hypothesis of the Augmented Dickey-Fuller 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 we cannot reject that there is a unit root.

The p-values are obtained through regression surface approximation from MacKinnon 1994, but using the updated 2010 tables. If the p-value is close to significant, then the critical values should be used to judge whether to accept or reject the null.

References

Greene Hamilton

P-Values (regression surface approximation) MacKinnon, J.G. 1994. “Approximate asymptotic distribution functions for unit-root and cointegration tests. Journal of Business and Economic Statistics 12, 167-76.

Critical values MacKinnon, J.G. 2010. “Critical Values for Cointegration Tests.” Queen’s University, Dept of Economics, Working Papers. Available at http://ideas.repec.org/p/qed/wpaper/1227.html

Examples

see example script

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