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Conserved Flux Renormalization

Conserved Flux Renormalization (CFR) is a trade-data feature that summarizes how traded value and trade-size entropy behave across multiple time scales inside each bar.

In practical Limen terms, CFR turns raw trades into:

  • a kline-like frame
  • plus six additional columns that describe multi-scale flow stability and entropy behavior

Use CFR when you want a compact diagnostic of whether trade flow looks scale-stable or anomalous inside each bar.

Input And Output​

Input​

conserved_flux_renormalization() expects a trade dataframe with at least:

  • datetime
  • price
  • quantity

Output​

It returns a kline-style dataframe containing:

  • datetime
  • open, high, low, close
  • volume
  • value_sum
  • vwap
  • flux_rel_std_mean
  • flux_rel_std_var
  • entropy_mean
  • entropy_var
  • Δflux_rms
  • Δentropy_rms

Usage​

from limen.features.conserved_flux_renormalization import conserved_flux_renormalization

cfr_df = conserved_flux_renormalization(
    trades_df,
    kline_interval='1h',
    base_window_s=60,
    levels=6,
)

Parameters​

ParameterMeaning
trades_dfraw trade dataframe
kline_intervalbar interval for the output frame, such as '1h'
base_window_ssmallest internal coarse-graining window in seconds
levelsnumber of renormalization levels to compute

What The CFR Columns Mean​

flux_rel_std_mean​

Mean relative variability of traded-value flux across the renormalization levels.

flux_rel_std_var​

Variance of that flux-variability ladder across levels.

entropy_mean​

Mean trade-size entropy across the renormalization levels.

entropy_var​

Variance of that entropy ladder across levels.

Δflux_rms​

Root-mean-square deviation from an ideal flat flux-variability ladder.

Higher values mean one or more scales dominate the traded-value flow instead of the flow looking scale-stable.

Δentropy_rms​

Root-mean-square deviation from an ideal one-bit-per-octave entropy ladder.

Higher values mean trade-size diversity changes unevenly across scales.

When CFR Is Useful​

Good fits:

  • anomaly detection in trade flow
  • regime features for microstructure-heavy experiments
  • identifying bars where traded value is concentrated on a few scales
  • identifying bars where trade-size diversity behaves unusually

Poor fits:

  • workflows where only OHLCV-level information is available
  • experiments that never touch raw trade data
  • cases where simpler activity features already capture the behavior you care about

The Intuition​

The conserved-flux idea treats traded value as conserved "stuff." Renormalization then asks:

what happens to that flow when we repeatedly zoom out in time?

The function starts from a base window such as 60 seconds and repeatedly coarse-grains the trade stream:

60s -> 120s -> 240s -> 480s -> ...

At each scale it measures two things:

  • how variable the traded-value flux is
  • how diverse the trade sizes are

Instead of returning the entire multi-scale ladder, CFR compresses it into a small set of summary features that can be used directly in downstream research.

Interpreting The Deviation Metrics​

The two most important anomaly-style outputs are:

  • Δflux_rms
  • Δentropy_rms

They measure how far the observed scale ladder is from an idealized reference shape.

As a rough intuition:

  • high Δflux_rms suggests bursty or scale-concentrated flow
  • high Δentropy_rms suggests an uneven or patchy size mix across scales
  • when both are elevated, the bar is more likely to be structurally unusual

These are interpretation aids, not hard universal thresholds.

  • Continue to Features for the broader feature layer CFR belongs to.
  • Continue to Historical Data if you need the trade-data surfaces CFR expects upstream.