FAMA (Following Adaptive Moving Average)

Scalar wrapper that exposes only the FAMA line from Mama. FAMA is MAMA's lagging companion in Ehlers' MESA construction — it uses half MAMA's adaptive alpha, so it reacts later than MAMA. MAMA crossing above FAMA marks a trend confirmation; MAMA below FAMA a reversal. This wrapper is useful when you want a single scalar smoother and don't need both MAMA and FAMA paired in one MamaOutput.

Quick reference

Item	Value
Family	Ehlers / Cycle (DSP)
Input type	f64
Output type	f64 (the FAMA scalar)
Output range	unbounded (price-units)
Default parameters	fast_limit = 0.5, slow_limit = 0.05 (Fama::classic())
Warmup period	Inherited from Mama — ~30 bars
Interpretation	Slower of the MAMA/FAMA pair; trend-confirmation line

Formula

(mama_t, fama_t) = Mama(x).update(x)
return fama_t

The internal Mama does all the work — Fama just discards the mama field of the output. See crates/wickra-core/src/indicators/fama.rs.

FAMA's recurrence inside Mama:

FAMA_t = 0.5 * alpha_t * MAMA_t + (1 - 0.5 * alpha_t) * FAMA_{t-1}

Half-alpha vs MAMA → roughly twice the lag.

Parameters

Name	Type	Default	Constraint	Description
fast_limit	f64	0.5	finite, 0 < slow < fast ≤ 1	Upper bound on adaptive alpha (forwarded to Mama).
slow_limit	f64	0.05	finite, 0 < slow < fast	Lower bound on adaptive alpha (forwarded to Mama).

Forwards Mama::new's validation errors. Fama::classic() returns the canonical (0.5, 0.05) factory.

Inputs / Outputs

Indicator<Input = f64, Output = f64>. Python: FAMA(fast, slow).batch(prices) returns a 1-D np.ndarray with NaN in the warmup prefix. Node: same shape; update(value) returns number | null.

Warmup

Same as Mama — the Hilbert chain needs ~30 bars to fill before adaptive alpha kicks in. warmup_period() delegates to the inner Mama.

Edge cases

• Constant input. FAMA converges to the constant.
• Reset. reset() clears the inner Mama state and last_value.
• Identity with MAMA's fama field. Fama::update(x) is exactly Mama::update(x)?.fama. There is no recomputation hidden inside the wrapper.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let prices: Vec<f64> = (0..200)
        .map(|i| 100.0 + (f64::from(i) * 0.2).sin() * 5.0)
        .collect();
    let mut f = Fama::classic();
    let out = f.batch(&prices);
    println!("row 100 FAMA = {:?}", out[100]);
    Ok(())
}

Python

import numpy as np
import wickra as ta

prices = 100 + np.sin(np.linspace(0, 30, 200)) * 5
fama = ta.FAMA(0.5, 0.05)
out = fama.batch(prices)
print('row 100:', out[100])

Node

const wickra = require('wickra');

const fama = new wickra.FAMA(0.5, 0.05);
const prices = Array.from({ length: 200 },
  (_, i) => 100 + Math.sin(i * 0.2) * 5);
console.log('row 100:', fama.batch(prices)[100]);

Streaming

use wickra::{Fama, Indicator};

let mut fama = Fama::classic();
let price_stream: Vec<f64> = Vec::new(); // your live price feed
for px in price_stream {
    if let Some(v) = fama.update(px) {
        // FAMA as a slow trend reference line
    }
}

Interpretation

• Slow line of the MAMA/FAMA pair. Use FAMA when you need a single smoothed reference and the MAMA line itself isn't required. E.g. price > FAMA as a coarse bull-trend filter.
• Confirmation, not signal. Trend confirmation systems use the crossing of MAMA over FAMA — but for that you want the paired MamaOutput from Mama directly, not this wrapper.
• Adaptive lag. FAMA's lag is variable: faster in trends, slower in cycles. The half-alpha vs MAMA ratio holds, so the relative lag is constant even as the absolute lag varies.

Common pitfalls

• Using FAMA alone for crossover signals. A crossover needs two lines. Fama is one — pair it with price, Sma, or Ema, or use Mama directly.
• Expecting a fixed period. There is no "period" parameter; FAMA's effective period varies with the underlying phase adaptation.
• Mismatched parameters with paired MAMA. If you instantiate both Mama and Fama independently, ensure the (fast_limit, slow_limit) tuples match — otherwise the two lines won't be comparable.

References

• John F. Ehlers, Cycle Analytics for Traders, Wiley (2013), ch. 8 — derives the MAMA/FAMA pair.

See also

• Mama — the parent indicator that emits both lines together.
• HilbertDominantCycle — underlying phase-extraction engine.
• Indicators-Overview — full taxonomy.