ADFULLER

This function applies the Augmented Dickey-Fuller (ADF) test to evaluate whether a univariate time series contains a unit root.

The null hypothesis is that the series is non-stationary with a unit root, while the alternative is stationarity.

It returns the test statistic, p-value, lag usage, sample size, and critical values used for interpretation.

Excel Usage

=ADFULLER(x, maxlag, adf_regression, adf_autolag, store, regresults)

x (list[list], required): Time-series observations as a 2D range.
maxlag (int, optional, default: null): Maximum lag included in the test regression; null uses default rule.
adf_regression (str, optional, default: “c”): Deterministic terms included in the test regression (c, ct, ctt, or n).
adf_autolag (str, optional, default: “AIC”): Automatic lag-selection criterion (AIC, BIC, t-stat, or none).
store (bool, optional, default: false): Return result storage object in addition to scalar outputs.
regresults (bool, optional, default: false): Return full regression results when available.

Returns (list[list]): 2D key-value table summarizing ADF statistics and critical values.

Example 1: ADF test with default regression and autolag

Inputs:

x										maxlag	adf_regression	adf_autolag	store	regresults
1	1.2	1.1	1.3	1.25	1.35	1.3	1.4	1.38	1.45		c	AIC	false	false

Excel formula:

=ADFULLER({1,1.2,1.1,1.3,1.25,1.35,1.3,1.4,1.38,1.45}, , "c", "AIC", FALSE, FALSE)

Expected output:

Result
adf_stat	-2.1749
p_value	0.21548
usedlag	3
nobs	6
critical_1%	-5.35426
critical_5%	-3.64624
critical_10%	-2.9012
icbest	-37.0965

Example 2: ADF test with constant and trend regression

Inputs:

x										maxlag	adf_regression	adf_autolag	store	regresults
2	2.1	2.05	2.2	2.15	2.25	2.3	2.35	2.32	2.4	2	ct	BIC	false	false

Excel formula:

=ADFULLER({2,2.1,2.05,2.2,2.15,2.25,2.3,2.35,2.32,2.4}, 2, "ct", "BIC", FALSE, FALSE)

Expected output:

Result
adf_stat	-5.66528
p_value	0.0000107685
usedlag	0
nobs	9
critical_1%	-5.49966
critical_5%	-4.07211
critical_10%	-3.4935
icbest	-26.0036

Example 3: ADF test using fixed lag count

Inputs:

x										maxlag	adf_regression	adf_autolag	store	regresults
3	2.9	3.1	3	3.2	3.1	3.3	3.25	3.35	3.3	1	c	none	false	false

Excel formula:

=ADFULLER({3,2.9,3.1,3,3.2,3.1,3.3,3.25,3.35,3.3}, 1, "c", "none", FALSE, FALSE)

Expected output:

Result
adf_stat	-1.29158
p_value	0.633016
usedlag	1
nobs	8
critical_1%	-4.66519
critical_5%	-3.36719
critical_10%	-2.80296

Example 4: ADF test without deterministic terms

Inputs:

x										maxlag	adf_regression	adf_autolag	store	regresults
1	0.95	1.02	0.98	1.01	0.99	1.03	1	1.04	1.01	1	n	AIC	false	false

Excel formula:

=ADFULLER({1,0.95,1.02,0.98,1.01,0.99,1.03,1,1.04,1.01}, 1, "n", "AIC", FALSE, FALSE)

Expected output:

Result
adf_stat	2.85276
p_value	0.999591
usedlag	1
nobs	8
critical_1%	-2.90189
critical_5%	-1.96617
critical_10%	-1.57649
icbest	-46.7118

Python Code

import numpy as np
from statsmodels.tsa.stattools import adfuller as sm_adfuller

def adfuller(x, maxlag=None, adf_regression='c', adf_autolag='AIC', store=False, regresults=False):
    """
    Run the Augmented Dickey-Fuller unit-root test for stationarity diagnostics.

    See: https://www.statsmodels.org/stable/generated/statsmodels.tsa.stattools.adfuller.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        x (list[list]): Time-series observations as a 2D range.
        maxlag (int, optional): Maximum lag included in the test regression; null uses default rule. Default is None.
        adf_regression (str, optional): Deterministic terms included in the test regression (c, ct, ctt, or n). Valid options: Constant, Constant+Trend, Constant+Trend+Quadratic, None. Default is 'c'.
        adf_autolag (str, optional): Automatic lag-selection criterion (AIC, BIC, t-stat, or none). Valid options: AIC, BIC, t-stat, None. Default is 'AIC'.
        store (bool, optional): Return result storage object in addition to scalar outputs. Default is False.
        regresults (bool, optional): Return full regression results when available. Default is False.

    Returns:
        list[list]: 2D key-value table summarizing ADF statistics and critical values.
    """
    try:
        def to1d(values):
            if isinstance(values, list):
                if all(isinstance(row, list) for row in values):
                    raw = [item for row in values for item in row]
                else:
                    raw = values
            else:
                raw = [values]

            out = []
            for item in raw:
                try:
                    out.append(float(item))
                except (TypeError, ValueError):
                    continue
            return out

        if adf_regression not in ("c", "ct", "ctt", "n"):
            return "Error: regression must be one of 'c', 'ct', 'ctt', or 'n'"

        if adf_autolag in ("none", "None", "", None):
            autolag_arg = None
        elif adf_autolag in ("AIC", "BIC", "t-stat"):
            autolag_arg = adf_autolag
        else:
            return "Error: autolag must be 'AIC', 'BIC', 't-stat', or 'none'"

        series = to1d(x)
        if len(series) < 4:
            return "Error: x must contain at least four numeric values"

        result = sm_adfuller(
            np.asarray(series, dtype=float),
            maxlag=maxlag,
            regression=adf_regression,
            autolag=autolag_arg,
            store=store,
            regresults=regresults,
        )

        adf_stat = float(result[0])
        p_value = float(result[1])
        usedlag = int(result[2])
        nobs_used = int(result[3])
        crit_values = result[4]

        rows = [
            ["adf_stat", adf_stat],
            ["p_value", p_value],
            ["usedlag", usedlag],
            ["nobs", nobs_used],
        ]

        if isinstance(crit_values, dict):
            for key in ("1%", "5%", "10%"):
                if key in crit_values:
                    rows.append([f"critical_{key}", float(crit_values[key])])

        if len(result) > 5 and isinstance(result[5], (int, float, np.floating)):
            rows.append(["icbest", float(result[5])])

        return rows
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

x *

Time-series observations as a 2D range.

maxlag

Maximum lag included in the test regression; null uses default rule.

adf_regression

Deterministic terms included in the test regression (c, ct, ctt, or n).

adf_autolag

Automatic lag-selection criterion (AIC, BIC, t-stat, or none).

store

Return result storage object in addition to scalar outputs.

regresults

Return full regression results when available.