Dickey–fuller test
A test for a unit root: regress the first-differenced series on its own lagged level and test whether the slope is zero. It uses its own critical values, because the usual t-test is invalid under the null.
Where you will meet it
Dickey–fuller test appears in 3 learning outcomes on the CFA syllabus. A few of them:
- Explain what unit roots mean for time-series work, when they tend to arise and how to detect them, and show how to transform a series with a unit root so that an AR model can be used on it
“Standard t-tests on b1 cannot detect the problem, so a Dickey–Fuller test is used.”
- Set out the stages of testing a series for a unit root (nonstationarity) and explain how the test connects to autoregressive models
“The Dickey–Fuller test rewrites the AR(1) model by subtracting x(t − 1) from both sides: x(t) − x(t − 1) = b0 + g1x(t − 1) + ε, where g1 = b1 − 1.”
- Explain how to check time-series variables for cointegration and/or nonstationarity before putting them into a linear regression
“Test with the Engle–Granger method: apply a Dickey–Fuller test to the regression residuals, using Engle–Granger critical values.”
See also
Critical value · T-test · Unit root
Practise it
Practise dickey–fuller test until it is automatic: questions that explain every wrong option.
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