How to use Cointegration Half-Life Solver
Engle-Granger residual ADF plus Ornstein-Uhlenbeck half-life from any two price or return series. The page reports hedge ratio, p-value, and a spread chart so you can size up the trade before sizing the trade.
What It Does
Use the calculator with intent
Engle-Granger residual ADF plus Ornstein-Uhlenbeck half-life from any two price or return series. The page reports hedge ratio, p-value, and a spread chart so you can size up the trade before sizing the trade.
Stat-arb traders evaluating a candidate pair before committing to a full backtest who need the quick cointegration + half-life answer.
Interpreting Results
ADF p-value below 0.05 means cointegrated. Half-life sets the holding period — 5-day half-life is daily-strategy territory, 50-day is monthly. Hedge ratio is the dollar weight per unit of the second series.
Input Steps
Field by field
- 1
Upload data
Upload two price series for the candidate pair. The tool will normalize and align timestamps.
- 2
Run calculation
Run the cointegration test (Engle-Granger ADF on residuals from the cointegrating regression). The tool refuses to estimate half-life if the test rejects.
- 3
If
If cointegration passes, the tool fits the OU mean-reversion process and reports half-life with standard error.
- 4
Compare results
Compare half-life across rolling windows (1-year, 3-year, full sample). Stable half-life across windows = robust pair; unstable = the relationship is regime-dependent.
- 5
If
If half-life is under 30 days and cointegration is stable, the pair is a candidate for further backtesting. Above 90 days, alpha decays before transaction costs amortize.
Common Scenarios
Use realistic starting points
Short half-life pair
Half-life
3 trading days
Daily strategy is viable; turnover is high so transaction costs matter; expect plenty of trade signals per month.
Long half-life pair
Half-life
60 trading days
Monthly strategy; signals rare but durable. Holding-period matches the half-life — closing early gives up most of the mean-reversion.
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FAQ
Questions people ask next
The short answers readers usually want after the first pass.
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