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KalmanInnovationResidualBOCPD

Incremental, causal technical analysis documentation

Summary

KalmanInnovationResidualBOCPD chains a Kalman innovation z-score residual into ResidualBOCPD (bounded BOCPD). It detects Bayesian online changepoints in the filter innovation process and returns signal, change probability (score), and residual.

Update API

import rtta

ind = rtta.KalmanInnovationResidualBOCPD(
    max_run_length=128,
    hazard=0.01,
    threshold=0.5,
    min_variance=1e-6,
    initial_price=float("nan"),
    dt=1.0,
    measurement_variance=0.25,
    fillna=True,
)
result = ind.update(close)
# result.signal, result.score (= probability), result.residual

Non-finite innovations skip BOCPD and return zero signal/score with the residual echoed.

Theory Of Operation

Same residual construction as KalmanInnovationResidualFOCuS: a constant-velocity Kalman filter produces \(\rho_t = \nu_t / \sqrt{S_t}\). Instead of FOCuS GLR, BOCPD places a posterior on residual run length and flags a changepoint when \(P(r_t=0) \ge \tau\). This is complementary to FOCuS: BOCPD models hazard and online residual mean/variance per hypothesis rather than a fixed Gaussian CUSUM threshold.

Recurrence

1. Innovation z-score \(\rho_t\) as in KalmanInnovationZScore / residual-FOCuS docs:

\[\nu_t = c_t - H\hat{x}_{t|t-1},\qquad \rho_t = \nu_t / \sqrt{H P_{t|t-1} H^\top + R}.\]

2. ResidualBOCPD on \(\rho_t\) with parameters (max_run_length, hazard, threshold, min_variance) — full recurrence in residual-bocpd.md / bounded-bocpd.md:

\[\mathrm{score}_t = \pi_t(0),\qquad \mathrm{signal}_t = \mathbf{1}\{\pi_t(0) \ge \tau\},\qquad \mathrm{residual}_t = \rho_t.\]

Implementation Notes

The recurrence is implemented in src/rtta/indicator.cpp in class KalmanInnovationResidualBOCPD (KalmanInnovationZScore innov_ + ResidualBOCPD bocpd_). Result type is InnovationChangepointResult (score holds BOCPD probability).

Reference