Unit Root Tests With Structural Breaks

An ordinary unit root test like the Augmented Dickey-Fuller test asks whether a series drifts randomly forever (a "unit root," meaning shocks never fully fade) or reverts to a stable level. A single structural break — a one-time shift, like a series jumping to a new average level after a regime change — can fool the standard test into concluding there's a unit root even when the series is actually stationary around two different levels, one before the break and one after.

The intuition for why this happens: think of a series that sits flat around 100 for years, then jumps to sit flat around 130 after some event, and stays flat there. To an ADF test that doesn't know about the break, that single jump looks statistically similar to the kind of persistent, ever-larger wandering a genuine unit-root series would produce, because the test is measuring how slowly deviations from a single fitted mean die out, and one big jump inflates that measure enormously.

Perron's break-aware test fixes this by first estimating where the break occurred (either fixed at a known date, like a specific known regime change, or estimated from the data as whichever candidate date maximizes the test's power) and then testing for a unit root around a mean that's allowed to shift at that point, so a single one-off jump no longer masquerades as permanent random drift. A worked illustration: a series with true mean 100 for periods 1–50 and mean 130 for periods 51–100 will typically fail to reject a unit root under standard ADF, but will correctly reject it once the break at period 50 is accounted for.