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
maxlag : int
regression : str {‘c’,’ct’,’ctt’,’nc’}
autolag : {‘AIC’, ‘BIC’, ‘t-stat’, None}
store : bool
regresults : bool
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Returns : | adf : float
pvalue : float
usedlag : int
nobs : int
critical values : dict
icbest : float
regresults : RegressionResults instance
resstore : (optional) instance of ResultStore
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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