adfuller

adfuller(X, [maxLag], [regression="c"], [autoLag="aic"], [store=false], [regResults=false])

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

The DolphinDB adfuller function is consistent with statsmodels.tsa.stattools.adfuller in terms of core algorithm and parameter design. The main difference lies in the return value structure:

• DolphinDB returns a structured dictionary with clear field semantics, which is convenient for engineering and programmatic processing.
• statsmodels returns a tuple; a ResultStore object can provide more detailed statistical information, making it more suitable for analytical scenarios.

X is a numeric vector indicating the time series data to test. The elements in X cannot be all identical, and null values are not supported.

maxlag (optional) is a non-negative integer indicating the maximum lag which is included in test. The default value is 12*(nobs/100)^{1/4} where nobs is the number of observations.

regression (optional) is a string indicating the constant and trend order to include in regression. It can be:

• "c" : constant only (default).

• "ct" : constant and trend.

• "ctt" : constant, and linear and quadratic trend.

• "n" : no constant, no trend.

autoLag (optional) is a string indicating the method to use when automatically determining the lag length among the values 0, 1, …, maxlag. It can be:

• "aic": The number of lags is chosen to minimize the Akaike information criterion.

• "bic": The number of lags is chosen to minimize the Bayesian information criterion.

• "tstat": Start with maxLag and drops a lag until the t-statistic on the last lag length is significant using a 5%-sized test.

• "max": The number of included lags is set to maxLag.

store (optional) is a Boolean value. If set to true, the regression result is returned additionally to the adf statistic. The default value is false.

regResults (optional) is a Boolean value. If set to true, the full regression results are returned. The default value is false.

A dictionary containing the following keys

• adfStat: A floating-point scalar indicating the test statistic.

• pValue: A floating-point scalar indicating the MacKinnon's approximate p-value based on MacKinnon (1994, 2010).

• usedLag: An integer indicating the number of lags used.

• nobs: An integer indicating the number of observations used for the ADF regression and calculation of the critical values.

• criticalValues: A dictionary containing the critical values for the test statistic at the 1 %, 5 %, and 10 % levels.

• icBest: A floating-point scalar indicating the maximized information criterion if autoLag is not max.

• resultStore: A dictionary with results when regResults or store is set to true.

data = 234 267 289 301 312 323 334 345 356 367
adfuller(data);

A dictionary is returned:

adfStat->-4.34190584894534
pValue->0.00037562619202430314
criticalValues->[-4.473135048010974,-3.2898806035665293,-2.772382345679012]
usedLag->0
nobs->9
icBest->-195.23465793624445