The Augmented Dickey-Fuller Test

Man processing lots of information to see solution
Mitch Blunt / Getty Images

Named for American statisticians David Dickey and Wayne Fuller who developed the test in 1979, the Dickey-Fuller test is used to determine whether a unit root, a feature that can cause issues in statistical inference, is present in an autoregressive model. The formula is appropriate for trending time series like asset prices. It is the simplest approach to test for a unit root, but most economic and financial times series have a more complicated and dynamic structure than can be captured by a simple autoregressive model, which is where the augmented Dickey-Fuller test comes into play.

Development

With a basic understanding of that underlying concept of the Dickey-Fuller test, it is not difficult to jump to the conclusion that an augmented Dickey-Fuller test (ADF) is just that: an augmented version of the original Dickey-Fuller test. In 1984, the very same statisticians expanded their basic autoregressive unit root test (the Dickey-Fuller test) to accommodate more complex models with unknown orders (the augmented Dickey-Fuller test).

Similar to the original Dickey-Fuller test, the augmented Dickey-Fuller test is one that tests for a unit root in a time series sample. The test is used in statistical research and econometrics, or the application of mathematics, statistics, and computer science to economic data.

The primary differentiator between the two tests is that the ADF is utilized for a larger and more complicated set of time series models. The augmented Dickey-Fuller statistic used in the ADF test is a negative number, and the more negative it is, the stronger the rejection of the hypothesis that there is a unit root.

Of course, this is only at some level of confidence. That is to say that if the ADF test statistic is positive, one can automatically decide not to reject the null hypothesis of unit root. In one example, with three lags, a value of -3.17 constituted rejection at the p-value of .10.

Other Unit Root Tests

By 1988, statisticians Peter C.B.

Phillips and Pierre Perron developed their Phillips-Perron (PP) unit root test. Though the PP unit root test is similar to the ADF test, the primary difference is in how the tests each manage serial correlation. Where the PP test ignores any serial correlation, the ADF uses a parametric autoregression to approximate the structure of errors. Oddly enough, both test typically end with the same conclusions, despite their differences.

Related Terms

  • Unit root: The primary concept for which the test was designed to investigate.
  • Dickey-Fuller test: To fully understand the augmented Dickey-Fuller test, one must first understand the underlying concepts and shortfalls of the original Dickey-Fuller test.
  • P-value: P-values are an important number in hypothesis tests.

Related Books

  • Greene, William H.. 1997. Econometric Analysis. 3nd edition.
    Macmillan Publishing Company.