Augmented Dickey-Fuller (ADF) Unit Root Test
Augmented Dickey-Fuller Unit Root Test · Also known as: ADF test, ADF unit root test, Dickey-Fuller test (augmented), Said-Dickey test
The Augmented Dickey-Fuller test is the standard procedure for determining whether a univariate time series contains a unit root — that is, whether the series is non-stationary. It extends the original Dickey-Fuller test by including lagged difference terms that absorb serial correlation in the residuals, making the test valid for a wide range of time-series processes encountered in economics and finance.
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When to use it
Use the ADF test as a mandatory pre-step before fitting ARIMA, VECM, or cointegration models, and whenever a regression involves time-series variables that might share stochastic trends. It is appropriate for a single continuous time series of moderate to long length (typically T > 50). Prefer it over the original DF test whenever serial correlation is plausible. Do not use it as the sole test: supplement with the Phillips-Perron test (which uses a non-parametric correction instead of lag augmentation) and the KPSS test (which reverses the null to stationarity). Avoid relying on ADF alone when the series contains a structural break — power can collapse near the break; use the Zivot-Andrews test instead.
Strengths & limitations
- Corrects for serial correlation in residuals through lag augmentation, making it applicable to ARMA-type processes of unknown order.
- Three model specifications (none, constant, constant-plus-trend) cover all practically relevant deterministic scenarios.
- Critical values and p-values are tabulated and widely implemented in all major statistical packages (R, Stata, EViews, Python).
- Straightforward interpretation: reject the null means the series can be treated as stationary in subsequent modelling.
- Computationally trivial even for very long series.
- Low power in small samples (T < 50) and near-unit-root situations, leading to frequent failure to reject a false null.
- Size distortions arise if too few lags are selected, inflating the probability of falsely concluding stationarity.
- Cannot detect stationarity around a structural break; a genuine break depresses power severely.
- Results are sensitive to the choice of deterministic components: including a trend when there is none (or omitting it when present) leads to incorrect inference.
- Assumes a single autoregressive unit root; it is not designed for seasonal unit roots or fractional integration.
Frequently asked
What does it mean if the ADF test fails to reject the null?
Failure to reject means the evidence is insufficient to conclude the series is stationary. This suggests a unit root is plausible; you should difference the series (or take logarithmic differences) before modelling. However, low power means you should corroborate with the PP test and visually inspect the series.
How many lags should I include in the ADF regression?
The most common automatic rule is to minimise AIC or BIC over a reasonable grid of lags (e.g., up to 12 for annual-frequency data, or int(12*(T/100)^0.25) for quarterly data). Always check that no significant autocorrelation remains in the ADF residuals.
What is the difference between ADF and Phillips-Perron?
Both test the same null of a unit root. ADF adds lagged differences to the regression to handle serial correlation parametrically; PP instead uses a non-parametric Newey-West correction to the test statistic. PP tends to be more powerful in large samples, but both can over-reject in small samples with severe moving-average components. Using both increases confidence.
Can I use ADF for panel data?
Standard ADF is designed for a single time series. For panel data use panel unit root tests such as Im-Pesaran-Shin (IPS), Levin-Lin-Chu (LLC), or Fisher-type tests, which pool information across cross-sectional units and have substantially better power.
What integration order should I assume if ADF rejects on the level but not on the first difference?
If the ADF rejects the unit root for the first difference (i.e., the differenced series is stationary) but fails to reject for the level, the series is integrated of order one, I(1). An I(1) series requires first-differencing before standard regression analysis, or it can enter a cointegration framework with other I(1) variables.
Sources
- Said, S. E., & Dickey, D. A. (1984). Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika, 71(3), 599–607. DOI: 10.1093/biomet/71.3.599 ↗
- 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. DOI: 10.2307/2286348 ↗
How to cite this page
ScholarGate. (2026, June 3). Augmented Dickey-Fuller Unit Root Test. ScholarGate. https://scholargate.app/en/econometrics/augmented-dickey-fuller-unit-root-test
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- ARIMA modelEconometrics↔ compare
- Engle-Granger Cointegration TestEconometrics↔ compare
- KPSS TestEconometrics↔ compare
- Phillips-Perron unit root testEconometrics↔ compare
- Zivot-Andrews Structural Break TestEconometrics↔ compare