Skip to content

RecursiveMedianOscillator

Ehlers DSP oscillator ehlers dsp median cycle highpass

Oscillator derived from the Recursive Median filter using a 2nd-order Highpass filter.

Visual Example

RecursiveMedianOscillator — 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

Oscillator derived from the Recursive Median filter using a 2nd-order Highpass filter.

Identify cyclic turning points with reduced lag and noise. The high-pass component removes the trend, leaving the cycle.

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.

By applying a 2nd-order Highpass filter to the Recursive Median output, we create an oscillator that is specifically tuned to the dominant cycle while remaining immune to the outlier spikes that would otherwise create false signals.

Typical applications:

  • Use for cycle timing in mean-reverting regimes
  • Gate with Hurst exponent or ADX before taking cycle signals
  • Allow 12+ 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/recursive_median.rs):

[ \alpha_2 = \frac{\cos(0.707 \cdot 360/HP) + \sin(0.707 \cdot 360/HP) - 1}{\cos(0.707 \cdot 360/HP)} ] [ RMO_t = (1-\alpha_2/2)^2(RM_t - 2RM_{t-1} + RM_{t-2}) + 2(1-\alpha_2)RMO_{t-1} - (1-\alpha_2)^2RMO_{t-2} ]

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

Parameters

Parameter Default Description
lp_period 12 Low-pass smoothing period
hp_period 30 High-pass cutoff period

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::RECURSIVE_MEDIAN_OSCILLATOR;
use quantwave_core::traits::Next;

let mut ind = RECURSIVE_MEDIAN_OSCILLATOR::new(12);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import RECURSIVE_MEDIAN_OSCILLATOR

ind = RECURSIVE_MEDIAN_OSCILLATOR(12)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_recursivemedianoscillator(series: pl.Series) -> pl.Series:
    ind = qw.RECURSIVE_MEDIAN_OSCILLATOR(12)
    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_recursivemedianoscillator, return_dtype=pl.Float64).alias("recursivemedianoscillator")
    )
    .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://www.traders.com/Documentation/FEEDbk_docs/2018/03/TradersTips.html

Implementation: quantwave-core/src/indicators/recursive_median.rs (RECURSIVE_MEDIAN_OSCILLATOR / RECURSIVE_MEDIAN_OSCILLATOR_METADATA). Parity: quantwave-core/tests/gold_standard/recursive_median_oscillator.json

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