Augmented Dickey-Fuller (ADF) Unit-Root Test
Also known as: ADF test, Dickey-Fuller test, unit root test, Genişletilmiş Dickey-Fuller testi
The Augmented Dickey-Fuller (ADF) test is the most widely used test for a unit root — that is, for whether a time series is non-stationary and must be differenced before modelling. Introduced by David Dickey and Wayne Fuller in 1979 and extended by Said and Dickey in 1984 to series with higher-order autocorrelation, it regresses the change in the series on its lagged level plus lagged differences and asks whether the lagged-level coefficient is zero.
Key highlights
- The de facto standard unit-root test, available in every econometrics package and widely understood by reviewers.
- The augmentation by lagged differences accommodates higher-order autocorrelation without modelling it explicitly.
- Flexible deterministic specification (constant, trend) lets it match a wide range of series behaviour.
- Provides a clear order-of-integration decision that feeds directly into ARIMA and cointegration analysis.
Intuition
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How it works
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When to use it
Apply the ADF test to any single time series before fitting models that assume stationarity, such as ARMA/ARIMA specification, regression among time series, or vector autoregressions — non-stationary inputs can produce spurious regressions. It is also the workhorse for determining the order of integration and as a building block of the Engle-Granger cointegration test. Choose the deterministic terms (none, constant, or constant-plus-trend) to match the visual behaviour of the series, and select the lag length to remove residual autocorrelation. Because the test has low power against near-unit-root (highly persistent but stationary) processes, pair it with a confirmatory KPSS test, whose null is the opposite, and with the Phillips-Perron test, which handles autocorrelation non-parametrically.
Strengths & limitations
- The de facto standard unit-root test, available in every econometrics package and widely understood by reviewers.
- The augmentation by lagged differences accommodates higher-order autocorrelation without modelling it explicitly.
- Flexible deterministic specification (constant, trend) lets it match a wide range of series behaviour.
- Provides a clear order-of-integration decision that feeds directly into ARIMA and cointegration analysis.
- Low power against persistent stationary alternatives: it often fails to reject a unit root that is not truly present.
- Results are sensitive to the chosen lag length and to whether a constant and trend are included.
- The non-standard Dickey-Fuller distribution must be used; ordinary t critical values are invalid.
- Structural breaks in the series can masquerade as a unit root, biasing the test toward non-rejection.
Common pitfalls
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Applications
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Frequently asked
What does failing to reject the ADF null mean?
It means there is insufficient evidence against a unit root, so the series is treated as non-stationary and usually differenced before modelling. Because the test has low power, failing to reject is not strong proof of a unit root — confirm with a KPSS test, which reverses the hypotheses.
How is the ADF test different from KPSS?
Their hypotheses are opposite. ADF takes non-stationarity (a unit root) as the null and looks for evidence of stationarity; KPSS takes stationarity as the null and looks for evidence of a unit root. Running both gives a more reliable, confirmatory conclusion about the order of integration.
Why can't I use ordinary t critical values?
Under the unit-root null the lagged level is a non-stationary regressor, so the t-ratio does not converge to a normal distribution. It follows the non-standard Dickey-Fuller distribution, whose critical values are more negative than the usual ones; using ordinary t values would reject far too often.
How many lagged differences should I include?
Enough to remove serial correlation from the residuals but no more, since extra lags cost power. Common practice is to select p by an information criterion (AIC/BIC) or a data-dependent rule, then verify the residuals are approximately white noise.
Sources
- 1.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(366a), 427–431.
- 2.Said, S. E., & Dickey, D. A. (1984). Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika, 71(3), 599–607.
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Cite this page
ScholarGate. (2026, June 2). Augmented Dickey-Fuller Test. ScholarGate. https://scholargate.app/econometrics/adf-test