Augmented Dickey-Fuller (ADF) unit-root test statistic

Computes the Augmented Dickey-Fuller test statistic for a unit root (non-stationarity) in a one-dimensional signal. The test regresses the first difference on a constant, the lagged level, and lag lagged first differences, \(\Delta y_t = \alpha + \beta y_{t-1} + \sum_{i=1}^{L} \gamma_i \Delta y_{t-i} + \varepsilon_t\), and returns the t-statistic on \(\beta\). A large negative statistic (below the Dickey-Fuller critical value) rejects the unit-root null in favour of stationarity. The statistic is the same deterministic OLS quantity as statsmodels.tsa.stattools.adfuller(..., autolag = None).

Usage

adfTest(x, lag = 1L)

Arguments

x: A numeric vector (the time series).
lag: Number of augmenting lagged differences \(L\) (default 1).

Value

A list with statistic (the ADF t-statistic on the lagged level), n (the regression sample size), and lag.

Details

Note: only the statistic is computed here (it is an exact regression quantity). The critical values and p-value require the Dickey-Fuller / MacKinnon reference tables (an approximation), so they are not returned; compare the statistic against the tabulated critical value for the decision.

References

Dickey, D.A., Fuller, W.A. (1979). Distribution of the estimators for autoregressive time series with a unit root. JASA, 74, 427-431.

Examples

set.seed(1)
adfTest(cumsum(rnorm(500)), lag = 1)$statistic   # random walk -> not far below 0
#> [1] -2.866323