Two independent asset-price paths can produce a persuasive level regression with no stable hedge behind it. A unit root invalidates familiar stationary-regression inference. This lesson distinguishes I(0) from I(1), explains spurious regression, and sets out DF, ADF, and Phillips–Perron tests. A stationary model can use I(0) levels directly. For I(1) levels, a stable equilibrium combination requires cointegration.
Learning objectives. By the end of this note you should be able to:
- define I(0), I(1), and a unit root; distinguish random walk with drift from trend-stationary;
- identify empirical symptoms of spurious regression;
- formulate DF/ADF hypotheses with correct deterministic terms and non-standard critical values;
- distinguish parametric ADF correction from Phillips–Perron's long-run-variance correction.
In this lesson
- Integrated processes
- Unit-root representation
- Spurious regression
- Dickey–Fuller
- ADF and Phillips–Perron
Before you start
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