adfuller

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

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.

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.

Return value: 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