Testing for Unit Roots: Dickey--Fuller, ADF, and Phillips--Perron

Before a desk differences a yield, price, or macro factor—or treats its level as a long-run signal—it needs evidence about the series’ integration order. A chart and a slowly decaying ACF cannot reliably separate a highly persistent stationary process from a unit root. Dickey--Fuller tests make that distinction explicit, while ADF and Phillips--Perron handle the serial dependence that financial data introduce.

• formulate the DF null and one-sided alternative in its regression form;
• choose deterministic terms consistent with the economic question;
• augment a DF regression and select its lag order;
• distinguish parametric ADF correction from PP’s long-run-variance correction;
• state why ordinary $t$ critical values are invalid.

1. From an AR coefficient to a unit-root test
2. ADF: make the residual innovation white
3. PP: robustify the statistic instead