ZeroLagMACD

The classic MACD topology with ZLEMA (zero-lag exponential moving average) substituted for EMA everywhere. The de-lagged construction of ZLEMA makes the MACD line react faster to trend changes at the cost of slightly noisier readings — particularly useful for shorter-timeframe systems where the standard MACD(12, 26, 9) signal arrives too late to be actionable.

Quick reference

Item	Value
Family	Price Oscillators
Input type	f64 (close)
Output type	ZeroLagMacdOutput { macd, signal, histogram }
Output range	unbounded; centred near zero
Default parameters	fast = 12, slow = 26, signal = 9 (ZeroLagMacd::classic())
Warmup period	zlema_warmup(slow) + zlema_warmup(signal) − 1 (50 for the classic configuration)
Interpretation	Same crossover semantics as MACD; ZLEMA substitution leads MACD by ~(period−1)/2 bars

Formula

ZLEMA_n(x) = zero-lag exponential moving average of x over n periods
             ZLEMA seeds from a simple average of the first n inputs,
             then applies the de-lagged recursion (Ehlers 2002).

macd_t   = ZLEMA_fast(close)_t  −  ZLEMA_slow(close)_t
signal_t = ZLEMA_signal(macd)_t
hist_t   = macd_t − signal_t

fast must be strictly less than slow. The signal ZLEMA does not start consuming inputs until macd_t becomes defined (i.e. until both the fast and slow ZLEMAs have seeded). The internal update feeds both inner ZLEMAs on every input so the slow one warms in parallel with the fast one (crates/wickra-core/src/indicators/zero_lag_macd.rs:92-105).

Parameters

Name	Type	Default	Constraint	Description
fast	usize	12	>= 1 and < slow	Fast ZLEMA period.
slow	usize	26	>= 1 and > fast	Slow ZLEMA period.
signal	usize	9	>= 1	ZLEMA period applied to the raw MACD line.

ZeroLagMacd::new returns Error::PeriodZero if any period is zero and Error::InvalidPeriod { message: "ZeroLagMACD fast period must be strictly less than slow" } if fast >= slow. ZeroLagMacd::classic() returns the (12, 26, 9) factory (zero_lag_macd.rs:78-80).

Inputs / Outputs

From impl Indicator for ZeroLagMacd:

use wickra::{Indicator, ZeroLagMacd, ZeroLagMacdOutput};
// ZeroLagMacd: Input = f64, Output = ZeroLagMacdOutput
const _: fn(&mut ZeroLagMacd, f64) -> Option<ZeroLagMacdOutput> = <ZeroLagMacd as Indicator>::update;

ZeroLagMacdOutput carries three fields:

Field	Description
macd	ZLEMA(fast) − ZLEMA(slow) of the input series.
signal	ZLEMA(signal) of macd.
histogram	macd − signal.

• Python. ZeroLagMACD.batch(prices) returns an (n, 3)float64 array with columns [macd, signal, histogram]; warmup rows are entirely NaN.
• Node. ZeroLagMACD.batch(prices) returns a flat number[] of length n * 3 with macd / signal / histogram interleaved at indices i*3, i*3+1, i*3+2. The streaming update(value) returns { macd, signal, histogram } | null.

Warmup

warmup_period() returns zlema_warmup(slow) + zlema_warmup(signal) − 1 where zlema_warmup(period) = (period − 1) / 2 + period. The first expression seats the slow ZLEMA; the signal ZLEMA then needs its own (period − 1) / 2 + period MACD values on top, minus 1 because the two phases overlap by exactly one bar.

Config	zlema_warmup(slow)	zlema_warmup(signal)	warmup
(12, 26, 9)	12 + 26 = 38	4 + 9 = 13	38 + 13 − 1 = 50
(3, 5, 3)	2 + 5 = 7	1 + 3 = 4	7 + 4 − 1 = 10

Pinned by the unit test warmup_period_matches_zlema_chain (zero_lag_macd.rs:213-225).

Edge cases

• Constant input. Each ZLEMA reproduces a constant, so macd approaches 0; with no movement in macd, the signal ZLEMA also approaches 0, and so does the histogram. Pinned by constant_series_converges_to_zero.
• Histogram identity. histogram == macd − signal is enforced by construction; the test histogram_is_macd_minus_signal checks it on a sine-wave price series.
• fast >= slow. Rejected by new; common bug when reading parameters from a config file.
• Reset. reset() resets all three inner ZLEMAs; the next warmup_period() updates return None again.
• Non-finite input. Delegated to the underlying ZLEMA; the EMA branch of ZLEMA preserves the previous value rather than poisoning the recursion with NaN.

Examples

Rust

use wickra::{BatchExt, Indicator, ZeroLagMacd};

fn main() {
    let prices: Vec<f64> = (1..=120)
        .map(|i| 100.0 + (f64::from(i) * 0.2).sin() * 5.0)
        .collect();
    let mut z = ZeroLagMacd::classic();
    let out = z.batch(&prices);
    let v = out[55].unwrap();
    println!("row 55  macd={:.6} signal={:.6} hist={:.6}",
             v.macd, v.signal, v.histogram);
}

Python

import numpy as np
import wickra as ta

prices = np.linspace(100.0, 120.0, 80)
z = ta.ZeroLagMACD(12, 26, 9)
out = z.batch(prices)
print('shape :', out.shape)        # (80, 3)
print('warmup:', z.warmup_period()) # 50
print('row 60:', out[60])           # macd, signal, hist

Node

const wickra = require('wickra');

const z = new wickra.ZeroLagMACD(12, 26, 9);
const prices = Array.from({ length: 80 }, (_, i) => 100 + i * 20 / 79);
const flat = z.batch(prices);
console.log('flat length:', flat.length); // 240
console.log('row 60:', flat[60 * 3], flat[60 * 3 + 1], flat[60 * 3 + 2]);

Streaming

use wickra::{Indicator, ZeroLagMacd};

let mut z = ZeroLagMacd::classic();
let price_stream: Vec<f64> = Vec::new(); // your live price feed
for px in price_stream {
    if let Some(v) = z.update(px) {
        if v.histogram > 0.0 && /* prev hist <= 0 */ true {
            // bullish histogram cross
        }
    }
}

Interpretation

• Signal-line crossover. As with MACD, macd crossing above signal is bullish; the symmetric crossover below is bearish. The histogram makes this explicit — it crosses zero on the same bar.
• Earlier than MACD. The ZLEMA substitution removes roughly (period − 1) / 2 bars of lag at each smoothing stage. For classic (12, 26, 9) parameters that means the ZeroLagMACD signal fires ~5-6 bars before MACD on a clean trend turn. The cost is a higher false-cross rate during chop.
• Pairs with MACD. Some traders run both indicators side by side: trade only when ZeroLagMACD and MACD agree on direction — ZeroLagMACD provides the early entry trigger, MACD provides the confirmation gate.

Common pitfalls

• Treating it as a drop-in MACD replacement. The warmup is longer (50 vs 34 for classic params) because ZLEMA's period + (period−1)/2 warmup is longer than EMA's period. Allocate enough history before the first signal.
• Misreading the "zero-lag" promise. ZLEMA reduces lag against a linear-trend reference; it does not eliminate it. Against a step-change input the response is still smoothed.
• Histogram-only systems. A histogram-zero-cross trigger on ZeroLagMACD fires more often than on MACD; pair it with a wider trend filter (e.g. a slow EMA slope, or ADX > threshold) to avoid whipsaw in ranges.

References

• John Ehlers, Rocket Science for Traders (2001), Chapter on ZLEMA / removing lag from EMAs.
• John Ehlers & Ric Way, Zero Lag (well, almost), Technical Analysis of Stocks & Commodities, November 2010 — refined treatment of the ZLEMA construction used here.
• Gerald Appel, Technical Analysis: Power Tools for Active Investors (2005) — canonical MACD topology that ZeroLagMACD inherits.

See also

• MacdIndicator — the EMA-based original this indicator de-lags.
• Zlema — the building block; understanding its warmup is key to understanding ZeroLagMACD's warmup.
• Stc — Schaff Trend Cycle, another faster-than-MACD alternative built on top of MACD.
• Indicators-Overview — full taxonomy.