QuanTAlib/lib/trends_IIR/mcnma/mcnma.pine

// Licensed under the Apache License, Version 2.0
// © mihakralj

//@version=6
indicator("MCNMA - McNicholl EMA", "MCNMA", overlay=true)

//@function Calculates the McNicholl EMA (Zero-Lag TEMA).
//  Dennis McNicholl, "Better Bollinger Bands," Futures Magazine, October 1998.
//  MCNMA = 2·TEMA(src,N) − TEMA(TEMA(src,N),N)
//  TEMA(x,N) = 3·EMA1 − 3·EMA2 + EMA3
//  Six cascaded EMA stages; na-guard init to source eliminates warmup bias.
//@param source Series to smooth
//@param period Lookback period (must be > 0)
//@returns McNicholl EMA value from bar 1
mcnma(series float source, simple int period) =>
    float src   = nz(source)
    float alpha = 2.0 / (period + 1)
    float beta  = 1.0 - alpha

    var float e1 = na
    var float e2 = na
    var float e3 = na
    var float e4 = na
    var float e5 = na
    var float e6 = na

    if na(e1)
        e1 := src
        e2 := src
        e3 := src
        e4 := src
        e5 := src
        e6 := src
    else
        e1 := alpha * src  + beta * e1
        e2 := alpha * e1   + beta * e2
        e3 := alpha * e2   + beta * e3

        float tema1 = 3.0 * e1 - 3.0 * e2 + e3

        e4 := alpha * tema1 + beta * e4
        e5 := alpha * e4    + beta * e5
        e6 := alpha * e5    + beta * e6

        float tema2 = 3.0 * e4 - 3.0 * e5 + e6

        // result is assigned below — but we need it outside the else
        // Pine requires expression, so use a different structure:

    // recompute after update (valid on all bars after init)
    float tema1 = 3.0 * e1 - 3.0 * e2 + e3
    float tema2 = 3.0 * e4 - 3.0 * e5 + e6
    2.0 * tema1 - tema2

// ── Inputs ─────────────────────────────────────────────────────────────
int    i_period = input.int(14, "Period", minval=1)
float i_source = input.source(close, "Source")

// ── Calculation ────────────────────────────────────────────────────────
float value = mcnma(i_source, i_period)

// ── Plot ───────────────────────────────────────────────────────────────
plot(value, "MCNMA", color.yellow, 2)