Time Series (Unit Roots, Autocorrelation)
Dickey-Fuller tests, spurious regression, HAC errors, the hazards of data over time.
Definition
Econometrics of ordered data: unit roots make series wander permanently, regressing two of them yields spurious correlations, and autocorrelated errors demand HAC standard errors.
Key equation
Dickey-Fuller: test ρ = 1 in y_t = ρy_{t−1} + u_t (nonstandard critical values)
The intuition
Two random walks will 'correlate' impressively while sharing nothing but drift, the spurious-regression trap that invalidates naive macro regressions. Difference the data (or find cointegration) before believing anything.
Exam tip
Workflow to recite: test for unit roots → if I(1), difference or test cointegration → then estimate, with HAC errors.
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