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ConformalBands

Incremental, causal technical analysis documentation

Summary

ConformalBands is RTTA's streaming split-conformal-style prediction band: an SMA center with a rolling quantile of absolute one-step residuals as radius. It is a lightweight band primitive, not a full adaptive conformal inference stack.

Update API

result = rtta.ConformalBands(window=20, alpha=0.1, fillna=True).update(value)
# result.middle, result.upper, result.lower, result.radius

alpha is the target non-coverage rate; the residual quantile level is \(1-\alpha\). Multi-output batch(...) returns arrays for middle, upper, lower, and radius.

Theory Of Operation

Conformal prediction forms a prediction set by calibrating nonconformity scores on recent data. For a simple one-step forecast, a common score is absolute residual \(\lvert y_t - \hat y_{t\mid t-1}\rvert\). RTTA uses the previous SMA value as \(\hat y\), stores absolute residuals in a rolling window, and takes a quantile at level \(1-\alpha\) as the radius around the current SMA center. This is intentionally simpler than adaptive conformal inference under distribution shift; it is a causal rolling calibration band.

Recurrence

Let \(x_t\) be the input, \(n\) be window, and \(q = 1-\alpha\).

  1. If a previous prediction \(\hat x_{t-1}\) exists, push residual \(s_t = \lvert x_t - \hat x_{t-1}\rvert\) into a rolling quantile store of capacity \(n\).
  2. Update the center:
\[m_t = \operatorname{SMA}_n(x_t)\]
  1. Set \(\hat x_t \leftarrow m_t\) for the next residual.
  2. Let \(R_t\) be the empirical quantile of stored absolute residuals at level \(q\) (RTTA RollingQuantile). Then
\[\begin{aligned} \operatorname{middle}_t &= m_t \\ \operatorname{radius}_t &= R_t \\ \operatorname{upper}_t &= m_t + R_t \\ \operatorname{lower}_t &= m_t - R_t \end{aligned}\]

With fillna=False, outputs are NaN until roughly \(n\) samples have been seen. Before residuals exist, the radius is treated as \(0\).

Implementation Notes

The recurrence is implemented in src/rtta/indicator.cpp in class ConformalBands using SMA and RollingQuantile. For a richer OHLCV composite that also uses residual quantiles for sizing, see MatchedFlowConformalSignal.

Reference