Trend vs. Difference Stationarity
Whether shocks die out or last forever, and why it changes how you model growth.
Definition
Whether shocks die out: trend-stationary series revert to a deterministic path (shocks temporary); difference-stationary series carry every shock forever (random walk with drift).
Key equation
TS: y_t = a + bt + u_t; DS: y_t = y_{t−1} + b + u_t
The intuition
Is a recession a detour or a new road? If GDP is trend-stationary it comes back; if difference-stationary, lost output is lost for good. The two look near-identical in samples yet imply opposite policy urgency.
Exam tip
Detrending handles TS but NOT DS series, differencing is the safe default when unit-root tests are ambiguous.
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