Direct Answer
The augmented Dickey-Fuller (ADF) statistic tests the null hypothesis that a series has a unit root, meaning it is non-stationary. It is the t-ratio on the lagged level in a regression that also includes lagged differences to absorb autocorrelation. More negative values are stronger evidence against a unit root.
Augmented Dickey-Fuller Statistic: Formula, Meaning, Signals, Examples and How to Use It
How Is Augmented Dickey-Fuller Statistic Calculated?
The augmented Dickey-Fuller (ADF) statistic tests the null hypothesis that a series has a unit root, meaning it is non-stationary. It is the t-ratio on the lagged level in a regression that also includes lagged differences to absorb autocorrelation.
Formula: delta y_t = alpha + beta*t + gamma*y_(t-1) + sum of delta_i * delta y_(t-i) + e_t; ADF = gamma_hat / se(gamma_hat)
Inputs:
- Series values
- Deterministic terms (none, constant, or constant and trend)
- Number of lagged differences
Worked example. A lagged-level coefficient of -0.045 with a standard error of 0.015 gives an ADF statistic of -3.00. The inputs are illustrative numbers, not market data.
Reading it. More negative values are stronger evidence against a unit root. The statistic follows a non-standard distribution; commonly cited asymptotic critical values for a constant-only regression are about -3.43 at 1 percent, -2.86 at 5 percent and -2.57 at 10 percent.
Limits. The test has low power against near-unit-root alternatives and is sensitive to the lag choice and structural breaks. Failing to reject does not prove non-stationarity.
What is Augmented Dickey-Fuller Statistic?
The augmented Dickey-Fuller (ADF) statistic tests the null hypothesis that a series has a unit root, meaning it is non-stationary. It is the t-ratio on the lagged level in a regression that also includes lagged differences to absorb autocorrelation.
How to use Augmented Dickey-Fuller Statistic
More negative values are stronger evidence against a unit root. The statistic follows a non-standard distribution; commonly cited asymptotic critical values for a constant-only regression are about -3.43 at 1 percent, -2.86 at 5 percent and -2.57 at 10 percent. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime.
Strengths
- Lagged differences in the regression absorb serial correlation, so the unit-root test works for more general series than the basic test.
- The statistic is a t-ratio, so it has a familiar form even though it is compared against special critical values.
- Reproducible when the formula and data convention are fixed.
Weaknesses and limitations
- Too many lag terms eat observations and weaken the test, while too few leave residual autocorrelation in the regression.
- Rejection applies to the specific regression form chosen, so a result with a trend term and one without can disagree.
- Correlated indicators can create false confidence by repeating the same underlying information.
Editorial and risk note
This page is educational content, not individualized investment advice. It should not imply guaranteed prediction, accuracy or outperformance.
Frequently Asked Questions
Is Augmented Dickey-Fuller Statistic a buy or sell signal?
No. More negative values are stronger evidence against a unit root. The test has low power against near-unit-root alternatives and is sensitive to the lag choice and structural breaks. A trade built on it still needs a trigger, an invalidation rule, a position size and realistic execution assumptions.
What is the best setting for Augmented Dickey-Fuller Statistic?
Augmented Dickey-Fuller Statistic is computed from series values; deterministic terms (none, constant, or constant and trend); number of lagged differences, so the choices that matter are the data convention and the window it is read over. Test those across instruments, regimes and out-of-sample periods instead of fitting one historical winner.
Can Augmented Dickey-Fuller Statistic be used by itself?
The test has low power against near-unit-root alternatives and is sensitive to the lag choice and structural breaks. Failing to reject does not prove non-stationarity. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone.
Does Augmented Dickey-Fuller Statistic work on every timeframe?
The calculation (delta y_t = alpha + beta*t + gamma*y_(t-1) + sum of delta_i * delta y_(t-i) + e_t; ADF = gamma_hat / se(gamma_hat)) can be run on any bar size, but behavior is not portable: a reading on a five-minute chart describes a very different market window from the same reading on a daily chart. Validate the exact timeframe before relying on it.
Why does Augmented Dickey-Fuller Statistic give false signals?
Too many lag terms eat observations and weaken the test, while too few leave residual autocorrelation in the regression. Rejection applies to the specific regression form chosen, so a result with a trend term and one without can disagree. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated.
How should Augmented Dickey-Fuller Statistic be backtested?
Rebuild Augmented Dickey-Fuller Statistic from series values using point-in-time data, write the rules before testing, include delisted securities where relevant, model realistic fills and costs, reserve a validation sample and compare with a simpler baseline.