Dickey-Fuller Test

A Dickey-Fuller Test is a stationarity test for AR(1).

• Context:
  • It can be a specialization of Augmented Dickey-Fuller.
  • …
• Counter-Example(s):
  • Phillips-Perron Test.
• See: Unit Root, Autoregressive, Alternative Hypothesis, Stationarity (Statistics), Trend Stationary.

---

---

References

2016

• (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/Dickey–Fuller_test Retrieved:2016-7-27.
  • In statistics, the Dickey–Fuller test tests the null hypothesis of whether a unit root is present in an autoregressive model. The alternative hypothesis is different depending on which version of the test is used, but is usually stationarity or trend-stationarity. It is named after the statisticians David Dickey and Wayne Fuller, who developed the test in 1979.

2008

• (Upton & Cook, 2008) ⇒ Graham Upton, and Ian Cook. (2008). “A Dictionary of Statistics, 2nd edition revised." Oxford University Press. ISBN:0199541450
  • QUOTE: A test for stationarity in a time series. The original test was designed to determine whether an AR(1) model was appropriate: :[math]\displaystyle{ X_j = \alpha X_{j-1} + \varepsilon_j. }[/math] Here [math]\displaystyle{ X_j }[/math] is the value at time [math]\displaystyle{ j, \alpha }[/math], is an unknown parameter and [math]\displaystyle{ \varepsilon_j. }[/math] is a random error. The test statistic is the product of the number of time points and [math]\displaystyle{ (\hat \alpha - 1) }[/math], where [math]\displaystyle{ \hat \alpha }[/math] is the ordinary least squares estimate of [math]\displaystyle{ \hat \alpha }[/math]. The test was extended in 1981 for use with other autoregressive models; the resulting test is called the augmented Dickey-Fuller test or the ADF test. The Phillips-Perron tests are related alternative tests suggested in 1988.

---