Talk:Dickey-Fuller test

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[edit] Implementation

How do one implement this test if one don't have a statistical software doing the job? Can anyone explain the test more in detail?

Your software just needs to be able to estimate a linear regression equation and calculate a t statistic. In addition, you need a table of Dickey-Fuller critical values; although the test statistic is calculated in the same way as an ordinary t statistic, it does not have the same distribution. Proceed as follows: (1) Difference your data series, ie calculate Δy_t = y_t − y_{t − 1} (2) Run a regression of Δy_t against y_{t − 1}, ie the differences against the lagged levels, with no constant. (3) If the reported t statistic is more negative than the critical value from the Dickey-Fuller table, reject the null hypothesis (that the series is non-stationary) in favour of the alternative (that it is stationary). If not, (4) re-run the regression with a constant; if the t statistic for y_{t − 1} is more negative than the critical value, reject the null hypothesis in favour of the alternative that the series is stationary about a linear trend. Note that the critical value varies with the presence or absence of the constant.