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RecursiveMedian

Ehlers DSP filter ehlers dsp median robust smoothing

EMA of a 5-bar median filter for smooth tracking with minimal jitter.

Visual Example

RecursiveMedian — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-06-25 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

The RecursiveMedian indicator is a technical analysis tool that ema of a 5-bar median filter for smooth tracking with minimal jitter.

This indicator is primarily used for identifying key market conditions. It provides a robust signal that can be easily integrated into both simple strategies and more complex machine learning feature pipelines. Compared to its alternatives, it offers a distinct balance of responsiveness and stability.

Traders often combine this with other metrics to confirm signals and avoid false positives during sideways market regimes. It remains a standard tool for systematic trading models.

Use to filter out extreme outliers and noise while maintaining trend sensitivity. Excellent as a baseline for other oscillators.

Standard filters like SMA or EMA are distorted by price spikes. The recursive median filter uses the median to reject outliers and an EMA to provide smoothness, offering a cleaner trend representation than standard moving averages.

QuantWave implements this indicator via the universal Next<T> trait, guaranteeing bit-identical results between Rust streaming, Python streaming, and Polars batch (.ta() / map_batches) surfaces.

Formula / Specification

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

[ \alpha = \frac{\cos(360/P) + \sin(360/P) - 1}{\cos(360/P)} ] [ RM_t = \alpha \cdot \text{Median}(Price, 5)t + (1 - \alpha) \cdot RM ]

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

Parameters

Parameter Default Description
lp_period 12 Low-pass smoothing period

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::RECURSIVE_MEDIAN;
use quantwave_core::traits::Next;

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

Streaming (Python)

from quantwave import RECURSIVE_MEDIAN

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

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_recursivemedian(series: pl.Series) -> pl.Series:
    ind = qw.RECURSIVE_MEDIAN(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_recursivemedian, return_dtype=pl.Float64).alias("recursivemedian")
    )
    .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 / RECURSIVE_MEDIAN_METADATA). Parity: quantwave-core/tests/gold_standard/recursive_median.json

Provenance: Standards bulk upgrade 2026-06-25 IST — see docs/DOCUMENTATION_STANDARDS.md.