When a levels regression of I(1) series is not spurious

Question

Two series Xt and Yt are each individually nonstationary (integrated of order 1), yet a levels regression of Yt on Xt is perfectly legitimate rather than spurious. What property must the regression residuals have for this to be the case?

Accepted Answer

The dividing line between a spurious regression and a valid one is the behavior of the residuals. - Spurious: the residuals are nonstationary (they inherit a unit root and wander like a random walk). The relationship is an illusion. - Valid: the residuals are stationary, that is, integrated of order 0, or I(0). They fluctuate around a fixed mean and never wander off. When two I(1) series have a linear combination that is stationary, they are said to be cointegrated. Intuitively, each series wanders on its own, but they wander together, staying tethered so that the gap between them (the residu…

When a levels regression of I(1) series is not spurious

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