Calculate the Augmented Dickey-Fuller (ADF) test for a unit root, per asset.

The test regresses the first difference of the series on its own lagged level and p lags of its own first difference. The null hypothesis is that the series has a unit root (is a random walk, not mean-reverting); the alternative is that it is stationary. This is a standard first step before modeling a price series or spread with mean-reverting methods, since those methods assume stationarity.

For more information about the method, see the following paper:

  • Dickey, D.A. and 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.

Also known as: ADF test, unit root test, stationarity test.

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Calculate the Augmented Dickey-Fuller (ADF) in Python

The Augmented Dickey-Fuller (ADF) is available in the Econometrics module of the open-source Finance Toolkit. Install it with:

pip install financetoolkit -U

Then call get_augmented_dickey_fuller as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(
    ["AMZN", "TSLA"],
    api_key="FINANCIAL_MODELING_PREP_KEY",
    start_date="2019-01-01",
    end_date="2023-12-31",
)

toolkit.econometrics.get_augmented_dickey_fuller(period="quarterly")

Which returns:

  AMZN TSLA
ADF Statistic -7.1569 -2.2371
P-Value 0 0.1931
Lags Used 8 8
Observations 11 11
Critical Value 1% -4.2232 -4.2232
Critical Value 5% -3.1894 -3.1894
Critical Value 10% -2.7298 -2.7298
Reject Unit Root (5%) 1 0

Parameters

get_augmented_dickey_fuller accepts the following parameters:

  • period (str, optional): The data frequency (daily, weekly, monthly, quarterly, or yearly). Defaults to “daily”.
  • column (str, optional): The historical data column to test. Defaults to “Adj Close”.
  • max_lag (int, optional): The maximum number of lagged differences to consider. Defaults to the Schwert (1989) rule of thumb.
  • regression (str, optional): Which deterministic terms to include, one of “n” (none), “c” (constant) or “ct” (constant and trend). Defaults to “c”.
  • include_benchmark (bool, optional): Whether to include “Benchmark” among the assets tested. Defaults to False.
  • rounding (int | None, optional): The number of decimals to round the results to. Defaults to None.

Related Unit Root & Stationarity

KPSS Test Phillips-Perron Test Zivot-Andrews Test Variance Ratio Test

The Econometrics module page introduces the module, and the sidebar lists all of its functions.

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