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Reversion Index

Ehlers DSP mean-reversion oscillator ehlers cycle

A mean-reversion oscillator that normalizes price changes by their absolute magnitude and applies SuperSmoother filtering.

Visual Example

Reversion Index — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-07-01 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

A mean-reversion oscillator that normalizes price changes by their absolute magnitude and applies SuperSmoother filtering.

Use to identify mean-reversion opportunities when price has deviated significantly from its cycle trend. High index values signal overextended moves ripe for reversal.

Part of QuantWave's Ehlers digital signal processing suite. Designed for low-lag cycle and trend work — pair with Roofing Filter or SuperSmoother on noisy inputs.

Ehlers Reversion Index measures how far price has deviated from its Instantaneous Trendline in units of cycle amplitude. Because it normalizes by the current cycle energy, the index provides consistent overbought/oversold thresholds regardless of the absolute price level or volatility regime.

Typical applications:

  • Use for cycle timing in mean-reverting regimes
  • Gate with Hurst exponent or ADX before taking cycle signals
  • Allow 20+ bars warm-up for filter state to stabilise
  • Chain with Roofing Filter when input is noisy

QuantWave implements this via the universal Next<T> trait — bit-identical across Rust streaming, Python streaming, and Polars .ta() batch plugins.

Formula / Specification

Implementation (quantwave-core/src/indicators/reversion_index.rs):

[ \Delta_t = \text{Close}t - \text{Close} ] [ \text{Ratio} = \frac{\sum_{i=0}^{L-1} \Delta_{t-i}}{\sum_{i=0}^{L-1} |\Delta_{t-i}|} ] [ \text{Smooth} = SuperSmoother(\text{Ratio}, 8) ] [ \text{Trigger} = SuperSmoother(\text{Ratio}, 4) ]

Gold-standard parity vectors: quantwave-core/tests/gold_standard/reversion_index.json.

Parameters

Parameter Default Description
length 20 Summation period (approx. half dominant cycle)

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::REVERSION_INDEX;
use quantwave_core::traits::Next;

let mut ind = REVERSION_INDEX::new(20);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import REVERSION_INDEX

ind = REVERSION_INDEX(20)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_reversion_index(series: pl.Series) -> pl.Series:
    ind = qw.REVERSION_INDEX(20)
    return pl.Series([ind.next(float(v)) for v in series.to_list()])

df = (
    pl.read_csv('ohlcv.csv')
    .lazy()
    .with_columns(
        pl.col("close").map_batches(apply_reversion_index, return_dtype=pl.Float64).alias("reversion_index")
    )
    .collect()
)

All surfaces are bit-identical via the single Next<T> implementation and proptests.

Edge Cases & Limitations

  • Recursive DSP filters require a warm-up period; first N bars may be unstable or raw-pass-through.
  • Designed for cyclic/mean-reverting regimes; trending markets can produce lag or drift.
  • Parameter period (or equivalent) controls cutoff — too small adds noise, too large adds lag.
  • Prefer chaining with other Ehlers tools (Roofing Filter, SuperSmoother) on noisy inputs.
  • Validated via proptests against gold-standard vectors where available.
  • No look-ahead bias; suitable for live streaming and batch feature pipelines.

Boundary Behavior

Condition Behavior
Warm-up Leading bars return NaN until warmup_bars is satisfied.
period > len When period exceeds series length, output is all NaN.
NaN inputs NaN in input propagates to output (NaN out).
Invalid params Non-positive period or missing required params raise ValueError.
Empty data Empty input returns an empty result series.

Sources & References

Primary Source: https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS%E2%80%99%20TIPS%20-%20JANUARY%202026.html

Implementation: quantwave-core/src/indicators/reversion_index.rs (REVERSION_INDEX / REVERSION_INDEX_METADATA). Parity: quantwave-core/tests/gold_standard/reversion_index.json

Provenance: Standards bulk upgrade 2026-07-01 IST — see docs/DOCUMENTATION_STANDARDS.md.