Empirical Capstone

A pairs or spot–futures study must distinguish a stable equilibrium residual from a spurious level fit. This capstone constructs a cointegrated pair with a known hedge ratio. It estimates the ratio on a formation sample, freezes the fit, and evaluates later one-step spread forecasts. Changing a model parameter then shows which conclusions depend on mean reversion and which depend on innovation variance.

• construct two I(1) legs sharing one common trend plus an I(0) gap;
• estimate a hedge ratio and interpret the residual as an equilibrium error;
• evaluate a one-step AR forecast of the spread under MSE;
• predict the effect of raising gap noise or weakening mean reversion on residual ACF and forecast error.

1. Constructed cointegrated pair
2. Python construction and hedge ratio
3. Unit-root-style check on the residual
4. Parameter checkpoint
5. Capstone workflow