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IntegratedOrderFlowImbalance

Incremental, causal technical analysis documentation

Summary

IntegratedOrderFlowImbalance projects multi-level Cont-style OFI onto an online first principal component of the level-event covariance. Each depth level contributes a rolling Cont event; an EMA covariance matrix and power-iteration weights form a single integrated scalar ofi plus the level-1 weight weight_l1.

Update API

import rtta

ind = rtta.IntegratedOrderFlowImbalance(
    levels=5, window=1, ema_alpha=0.05, fillna=True
)
result = ind.update(bid_price, bid_size, ask_price, ask_size)  # vectors length `levels`
# result.ofi, result.weight_l1

batch = ind.batch(bid_prices, bid_sizes, ask_prices, ask_sizes)  # (n, levels)

advance(...) updates state without returning a result. Float32/float64 depth vectors and batch matrices are supported.

Theory Of Operation

Raw multi-level OFI is a vector \(v_t \in \mathbb{R}^L\). In practice the components are highly collinear; Cont-style “integrated” OFI collapses depth into one factor by taking the leading eigenvector of the event covariance and the corresponding linear combination. RTTA maintains:

  1. Per-level Cont events and rolling sums \(v^{(\ell)}_t\) (same map as multi-level OFI).
  2. An exponential moving covariance \(\Sigma_t\) of the vector \(v_t\).
  3. Four power-iteration steps on \(\Sigma_t\) starting from the previous weight vector, re-oriented so the top-of-book weight is non-negative.
  4. Scalar projection \(\mathrm{ofi}_t = w_t^\top v_t\).

Initial weights are \(w = (1,0,\ldots,0)\). With fillna=False, outputs are NaN until count >= window.

Recurrence

Cont events \(e^{(\ell)}_t\) and rolling sums \(v^{(\ell)}_t = S^{(\ell)}_t\) are identical to MultiLevelOrderFlowImbalance (with incomplete windows forced to \(0\) when building \(v\) under fillna=True logic that uses the sum when the window is not full only if fillna).

Covariance EMA with \(\alpha = \mathrm{ema\_alpha}\) (clamped to \([10^{-6},1]\)):

\[\Sigma_t = (1-\alpha)\,\Sigma_{t-1} + \alpha\, v_t v_t^\top.\]

Power iteration (four steps) from previous weights \(w_{t-1}\):

\[\tilde{w}^{(0)} = w_{t-1},\qquad \tilde{w}^{(k+1)} = \frac{\Sigma_t \tilde{w}^{(k)}}{\|\Sigma_t \tilde{w}^{(k)}\|_2}, \quad k=0,1,2,3.\]

Sign flip so \(\tilde{w}^{(4)}_0 \ge 0\):

\[w_t = \begin{cases} -\tilde{w}^{(4)}, & \tilde{w}^{(4)}_0 < 0,\\ \tilde{w}^{(4)}, & \text{otherwise}. \end{cases}\]

Outputs:

\[\mathrm{ofi}_t = w_t^\top v_t,\qquad \mathrm{weight\_l1}_t = w_{t,0}.\]

If fillna=False and \(t < W\), both fields are NaN.

Implementation Notes

The recurrence is implemented in src/rtta/indicator.cpp in class IntegratedOrderFlowImbalance. Covariance is stored row-major as a length-\(L^2\) vector. Batch requires shape (n_samples, levels).

Reference