Talk:Dickey–Fuller test

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 $$\Delta y_t = y_t - y_{t-1}$$  (2) Run a regression of $$\Delta y_t$$ 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.


 * That's two models. What about the third, with a deterministic time trend?  Do you re-run the regression with a constant and a trend (0:n)?
 * Also, what you wrote seems to answer the question, what is the Dickey-Fuller test, which the article doesn't define. Shouldn't the article say what the Dickey-Fuller test actually is, as opposed to merely giving a few of its properties and motivation for it?  Vaughan Pratt (talk) 20:12, 18 July 2014 (UTC)

Problems
I just noticed link for reference 5 is broken. I'm not sure what's the right way to edit the page when that happens so I'm posting the problem here. — Preceding unsigned comment added by 190.250.147.133 (talk) 21:17, 27 November 2011 (UTC)
 * I have replaced the link with one that is presently live. Other links I found were not free access. Melcombe (talk) 10:03, 28 November 2011 (UTC)

Delta not Nabla?
Why does this page use the 'nabla' instead of a proper 'Delta' for differencing? Shabbychef (talk) 21:21, 17 January 2012 (UTC)
 * This article seems consistent with notation defined in the article finite difference, which uses the two different symbols for forward and backward differences. However, it is not clear that the notation attempts to be consistent with any particular one of the references included, as the definition is given without citations. Melcombe (talk) 22:57, 17 January 2012 (UTC)

Clarify Scope Of First Example
The article begins with an example of AR model and then mentions 3 versions of the test, but it does not make it clear (to those unfamiliar with AR models) whether all 3 versions of the test apply to the original example or whether there are different versions of the test because there are other AR models that differ from the initial example. If the article is to begin with examples, it would be best to give examples of all relevant AR models.

Since this article is about hypothesis tests, it would easier to read if it stated the null hypotheses and test statistics explicitly.

Tashiro (talk) 04:50, 30 November 2012 (UTC)

It would also help if the symbol "t" was not used ambiguously to denote both "the time index" and a statistic.

Tashiro~enwiki (talk) 06:27, 15 May 2016 (UTC)