PARKED · implementation
Hypothesis
The cointegration failure of static pairs (see N-018) is fixable: let the hedge ratio $\beta_t$ evolve as a hidden state estimated online with a Kalman filter, so the spread stays stationary as the relationship drifts.
Math — state-space hedge ratio
State (hidden hedge ratio) and observation (one leg priced off the other):
$$ \beta_t = \beta_{t-1} + w_t,\qquad y_t = \beta_t x_t + v_t $$
Kalman update for the posterior estimate:
$$ \hat\beta_t = \hat\beta_{t-1} + K_t\,(y_t - \hat\beta_{t-1}x_t) $$
Method
Process/observation noise $Q,R$ tuned by likelihood. Trade the standardized innovation $y_t-\hat\beta_{t-1}x_t$. Prototype only — not yet replayed on full out-of-sample with realistic costs.
Theoretically the correct fix for N-018’s drifting $\beta$. Parked pending a full path-dependent cost study — the open question is whether the adaptive ratio reduces drawdowns faster than it adds whipsaw. Queued behind higher-EV work.
When a static parameter is the failure mode, model it as a hidden state. But adaptivity is not free — it trades bias for variance, and variance is whipsaw.