statsmodels.tsa.stattools.adfuller¶
-
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
- xarray_like, 1d
The data series to test.
- maxlag
int
Maximum lag which is included in test, default 12*(nobs/100)^{1/4}.
- regression{‘c’,’ct’,’ctt’,’nc’}
Constant and trend order to include in regression.
‘c’ : constant only (default).
‘ct’ : constant and trend.
‘ctt’ : constant, and linear and quadratic trend.
‘nc’ : no constant, no trend.
- autolag{‘AIC’, ‘BIC’, ‘t-stat’,
None
} Method to use when automatically determining the lag.
if None, then maxlag lags are used.
if ‘AIC’ (default) or ‘BIC’, then the number of lags is chosen to minimize the corresponding information criterion.
‘t-stat’ based choice of maxlag. Starts with maxlag and drops a lag until the t-statistic on the last lag length is significant using a 5%-sized test.
- storebool
If True, then a result instance is returned additionally to the adf statistic. Default is False.
- regresultsbool,
optional
If True, the full regression results are returned. Default is False.
- Returns
- adf
float
The test statistic.
- pvalue
float
MacKinnon’s approximate p-value based on MacKinnon (1994, 2010).
- usedlag
int
The number of lags used.
- nobs
int
The 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.
- resstore
ResultStore
,optional
A dummy class with results attached as attributes.
- adf
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 reject the null.
The autolag option and maxlag for it are described in Greene.
References
- 1
Green. “Econometric Analysis,” 5th ed., Pearson, 2003.
- 2
Hamilton, J.D. “Time Series Analysis”. Princeton, 1994.
- 3
MacKinnon, J.G. 1994. “Approximate asymptotic distribution functions for unit-root and cointegration tests. Journal of Business and Economic Statistics 12, 167-76.
- 4
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 notebook