Glossary

Augmented Dickey-Fuller (ADF) Test

The ADF test is a widely used unit-root test that augments the basic Dickey-Fuller regression with lagged first differences of the dependent variable to account for serial correlation in the error term. Said and Dickey (1984) showed that approximating an ARMA process with a su...

Definition

The ADF test is a widely used unit-root test that augments the basic Dickey-Fuller regression with lagged first differences of the dependent variable to account for serial correlation in the error term. Said and Dickey (1984) showed that approximating an ARMA process with a sufficiently long autoregression yields a test statistic whose limiting distribution matches the standard Dickey-Fuller tables. The ADF test is typically the first step in time-series analysis to determine whether differencing is needed to achieve stationarity.

Why It Matters

Before estimating any time-series model, researchers must establish whether the data are stationary. Running regressions on non-stationary series can produce spurious results with misleadingly high R-squared values and significant t-statistics. The ADF test provides a formal, widely accepted procedure for this critical diagnostic step and is a prerequisite for cointegration analysis.

Example

A researcher studying the Turkish lira / US dollar exchange rate suspects the series has a unit root. Running an ADF test with a trend and four lagged differences yields a test statistic of -2.1, which is above the 5% critical value of -3.45. The null hypothesis of a unit root cannot be rejected, confirming that the series is non-stationary and must be differenced before further modelling.

Related Terms

Software Notes

  • SPSS: Analyze > Forecasting > Unit Root Test; select ADF and specify lag length or use automatic selection.
  • R: Use adf.test() from the tseries package or ur.df() from the urca package for more detailed output including lag selection.
  • Stata: Use dfuller variable, trend lags(4) for an ADF test with trend and 4 lags. Use dfuller variable, trend for automatic lag selection via the Ng-Perron criterion.