Direct Answer
The Engle-Granger cointegration statistic tests whether two non-stationary series share a stable long-run relationship. One series is regressed on the other and a Dickey-Fuller type test is run on the residuals; stationary residuals suggest cointegration. More negative statistics are stronger evidence that the residual is stationary.
Cointegration Statistic: Formula, Meaning, Signals, Examples and How to Use It
How Is Cointegration Statistic Calculated?
The Engle-Granger cointegration statistic tests whether two non-stationary series share a stable long-run relationship. One series is regressed on the other and a Dickey-Fuller type test is run on the residuals; stationary residuals suggest cointegration.
Formula: Step 1: y = a + b*x + e. Step 2: delta e_t = gamma * e_(t-1) + lags + u; statistic = gamma_hat / se(gamma_hat)
Inputs:
- Two price series
- Window length
- Lag length for the residual test
Worked example. A residual coefficient of -0.12 with a standard error of 0.04 gives a test statistic of -3.00. The inputs are illustrative numbers, not market data.
Reading it. More negative statistics are stronger evidence that the residual is stationary. The statistic must be compared with special critical values (MacKinnon) rather than standard Dickey-Fuller tables, because the residuals come from an estimated regression.
Limits. The result depends on which series is chosen as the dependent variable, and power is low in short samples. A relationship that passes in-sample can break later.
What is Cointegration Statistic?
The Engle-Granger cointegration statistic tests whether two non-stationary series share a stable long-run relationship. One series is regressed on the other and a Dickey-Fuller type test is run on the residuals; stationary residuals suggest cointegration.
How to use Cointegration Statistic
More negative statistics are stronger evidence that the residual is stationary. The statistic must be compared with special critical values (MacKinnon) rather than standard Dickey-Fuller tables, because the residuals come from an estimated regression. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime.
Strengths
- The residual test turns the question of a stable long-run link into a single statistic with tabulated critical values.
- Regressing one level series on another first removes the shared stochastic trend, so the residual test looks only at the leftover gap.
- Reproducible when the formula and data convention are fixed.
Weaknesses and limitations
- Critical values differ from standard Dickey-Fuller tables because the residuals come from a fitted regression, so the right table has to be used.
- Only one relationship between two series is tested, so with three or more variables it cannot count how many relationships exist.
- 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 Cointegration Statistic a buy or sell signal?
No. More negative statistics are stronger evidence that the residual is stationary. The result depends on which series is chosen as the dependent variable, and power is low in short samples. 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 Cointegration Statistic?
Cointegration Statistic takes these inputs: two price series; window length; lag length for the residual test. There is no universal best setting for the tunable ones, so test them across instruments, regimes and out-of-sample periods and favor stable parameter regions over one historical winner.
Can Cointegration Statistic be used by itself?
The result depends on which series is chosen as the dependent variable, and power is low in short samples. A relationship that passes in-sample can break later. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone.
Does Cointegration Statistic work on every timeframe?
The calculation (Step 1: y = a + b*x + e. Step 2: delta e_t = gamma * e_(t-1) + lags + u; statistic = 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 Cointegration Statistic give false signals?
Critical values differ from standard Dickey-Fuller tables because the residuals come from a fitted regression, so the right table has to be used. Only one relationship between two series is tested, so with three or more variables it cannot count how many relationships exist. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated.
How should Cointegration Statistic be backtested?
Rebuild Cointegration Statistic from two price series 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.