TradingCalcCointegration Test Calculator
RISK/STATS · COINTEGRATION · ADVANCED
Engle-Granger two-step cointegration test for a pair of price series: the standard pairs-trading signal, with the hedge ratio from the cointegrating regression.
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Comma, space, or newline separated. No thousand separators (write 43250.50, not 43,250.50).
Engle-Granger two-step test: OLS regression Y = alpha + beta*X, then an Augmented Dickey-Fuller test on the residuals. A significantly negative t-statistic (below the critical value) means the residual spread is stationary: Y and X are cointegrated.
The formula
Engle-Granger two-step procedure:
- Step 1: OLS regression Y = α + βX, giving the hedge ratio β
- Step 2: ADF test on the residuals: delta(e_t) = gamma × e_(t-1) + u_t
- t-stat = γ / SE(γ), compared against critical values at 1%/5%/10%
Reading the result
A t-statistic more negative than the critical value rejects the unit-root null: the residual spread is stationary, meaning Y and X are cointegrated at that significance level. The hedge ratio (β) is how many units of X to hold per unit of Y to build the spread.
Where to go next
Cointegration is a relationship between two series. For memory structure within a single series, see the Hurst exponent calculator, or size a position against tail risk with the VaR / CVaR calculator.
Use via API or MCP
This calculation is available as a deterministic API call for bots and AI agents.
What does "cointegrated" mean for a pair of assets?
Two price series are cointegrated if a specific linear combination of them is stationary (mean-reverting) even though each series individually is not (each may wander like a random walk). This is the statistical basis for pairs trading: if the spread reverts to its mean, deviations from that mean are a tradeable signal.
How does the Engle-Granger test work?
Two steps: (1) an OLS regression of one price series on the other, Y = alpha + beta*X, giving the hedge ratio beta; (2) an Augmented Dickey-Fuller test on that regression's residuals, testing whether the residual spread has a unit root (non-stationary, not cointegrated) or is stationary (cointegrated).
What does the hedge ratio (beta) mean in practice?
It's how many units of X to hold per unit of Y to construct the cointegrating spread (Y - beta*X). A pairs trade typically goes long the undervalued side and short beta units of the other when the spread deviates from its historical mean.
Why are the critical values different from a standard ADF test?
Testing the RESIDUALS of a prior regression (rather than testing a raw series directly) changes the test statistic's distribution: these are the MacKinnon critical values specific to the two-step Engle-Granger procedure, not the plain Dickey-Fuller table.
Correlation vs cointegration: aren't these the same thing?
No. Two series can be highly correlated in their day-to-day moves while drifting apart over the long run (not cointegrated), and two series can be weakly correlated day-to-day while still sharing a stable long-run relationship (cointegrated). Pairs trading specifically needs cointegration, not just correlation.