How does the augmented Dickey-Fuller (ADF) test work?

Question

AcadiFi · Accepted Answer

The augmented Dickey-Fuller test checks whether a time series has a unit root, i.e. whether it is non-stationary. The test regresses the first difference of the series on its lagged level plus additional lagged differences to control for higher-order autocorrelation. The regression: delta x_t equals alpha plus beta times x_{t-1} plus sum of gamma_i times delta x_{t-i} plus epsilon_t. The null hypothesis is H0: beta equals 0, meaning a unit root exists (non-stationary). The alternative is Ha: beta less than 0, meaning stationary. The test statistic is the t-statistic on beta, but the distribution is non-standard (tabulated Dickey-Fuller critical values, more negative than standard t). If the calculated t-statistic is more negative than the critical value, reject the null and conclude stationarity. Example: econometrician Osvaldo Mensah-Whitfield at Sunhaven Econ Partners tests 20 years of quarterly Lumera Index log-levels. ADF statistic equals negative 1.42, 5 percent critical value equals negative 2.86. Since negative 1.42 is greater than negative 2.86, fail to reject — the series has a unit root and is non-stationary. First-differencing yields returns with ADF statistic of negative 9.51 — clearly stationary. ```mermaid flowchart TD S[Series] --> A[Run ADF] A --> B{t-stat more neg
than critical?} B -->|Yes| C[Reject H0
Stationary] B -->|No| D[Fail to reject
Unit root] D --> E[Difference
retest] ``` Choose the lag order for augmentation via AIC or BIC to avoid residual autocorrelation contaminating the test.

How does the augmented Dickey-Fuller (ADF) test work?

Master Level II with our CFA Course

Related Questions

Practice Questions