Overview
A random walk yₜ = yₜ₋₁ + εₜ has a unit root; shocks never fade.
📌 At a glance
- Tests
- ADF, PP, KPSS
Why it matters
Regressing unit-root series invites spurious regression; Nelson and Plosser (1982) found many US macro series have unit roots.
Interpretation
Reject the ADF null → stationary. Use Dickey–Fuller critical values. If I(1), difference or test for cointegration.
ADF and KPSS can disagree. That usually signals low power or structural breaks.
Frequently asked questions
- Which software?
- statsmodels (adfuller, kpss) in Python; urca or tseries in R.
References
- Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366), 427–431.
- Said, S. E., & Dickey, D. A. (1984). Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika, 71(3), 599–607.
- Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346.
- Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1–3), 159–178.
- Nelson, C. R., & Plosser, C. I. (1982). Trends and random walks in macroeconomic time series. Journal of Monetary Economics, 10(2), 139–162.