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
The idea
A series has a unit root when its lag coefficient b1 equals 1. Unit roots are common in asset prices, exchange rates and other levels that wander without a fixed anchor, and they make the series non-stationary, so AR estimates and t-tests on it are invalid. Standard t-tests on b1 cannot detect the problem, so a Dickey–Fuller test is used. The fix is first-differencing: model the change, y(t) = x(t) − x(t − 1), which is stationary when x has a single unit root. Forecast the change with an AR model, then add it to the latest level to forecast the level. A slip is feeding a level into a model estimated on changes.
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