Set out the stages of testing a series for a unit root (nonstationarity) and explain how the test connects to autoregressive models
The idea
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. The null hypothesis is a unit root, with g1 equal to 0, and the alternative is stationarity, with g1 below 0. The t-statistic on g1 is compared with Dickey–Fuller critical values, which are more negative than ordinary t-values, so using the standard table rejects the unit root too often. Versions of the test can include an intercept, a trend, or extra lags. Failing to reject means the series should be differenced before modelling. A negative g1 estimate alone proves nothing.
In the app: 2 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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