Jurik Adaptive Envelope Bands

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Jurik Adaptive Envelope Bands", "JBANDS", overlay=true)

//@function Jurik Adaptive Envelope Bands - Upper/Lower bands from JMA's adaptive envelope tracking
//@param   source Series to calculate JBANDS from
//@param   period Number of bars used in the calculation (>= 1)
//@param   phase  Phase shift (-100 to 100). Negative = smoother, positive = more leading
//@returns Array of [middle (JMA), upper, lower]
jbands(series float source, simple int period, simple int phase = 0) =>
    // ---- Precomputed length/phase parameters (constant per series) ----
    simple float _PHASE      = phase < -100 ? 0.5 : phase > 100 ? 2.5 : (phase * 0.01) + 1.5
    simple float _LEN0       = period < 1.0000000002 ? 1e-10 : (period - 1.0) / 2.0
    simple float _LOG_PARAM  = math.max(math.log(math.sqrt(_LEN0)) / math.log(2.0) + 2.0, 0.0)
    simple float _SQRT_PARAM = math.sqrt(_LEN0) * _LOG_PARAM
    simple float _LEN_ADJ    = _LEN0 * 0.9
    simple float _LEN_DIV    = _LEN_ADJ / (_LEN_ADJ + 2.0)
    simple float _SQRT_DIV   = _SQRT_PARAM / (_SQRT_PARAM + 1.0)
    simple float _P_EXP      = math.max(_LOG_PARAM - 2.0, 0.5)

    // ---- Internal state (persists across bars) ----
    var float  upperBand   = na
    var float  lowerBand   = na
    var float  lastC0      = na
    var float  lastC8      = na
    var float  lastA8      = na
    var float  lastJma     = na
    var int    bars        = 0

    // 10-bar local deviation window
    var float  cycleDelta  = 0.0
    var int    volIndex    = 0
    var int    volCount    = 0
    var array<float> volWindow  = array.new_float(10, 0.0)

    // 128-bar volatility distribution
    var int    distIndex   = 0
    var int    distCount   = 0
    var array<float> distWindow = array.new_float(128, 0.0)
    var array<float> sorted     = array.new_float(0)

    float current_jma   = na
    float current_upper = na
    float current_lower = na

    if not na(source)
        bars += 1

        // ---- First bar: initialize anchors and filter state ----
        if bars == 1
            upperBand := source
            lowerBand := source
            lastC0    := source
            lastC8    := 0.0
            lastA8    := 0.0
            lastJma   := source
            current_jma   := source
            current_upper := source
            current_lower := source
        else
            // 1) Local deviation vs. UpperBand / LowerBand
            float diffA    = source - upperBand
            float diffB    = source - lowerBand
            float absA     = math.abs(diffA)
            float absB     = math.abs(diffB)
            float absValue = absA > absB ? absA : absB
            float dLocal   = absValue + 1e-10

            // 2) 10-bar SMA of local deviation -> highD
            float oldVol = array.get(volWindow, volIndex)
            cycleDelta  += dLocal - oldVol
            array.set(volWindow, volIndex, dLocal)
            volIndex += 1
            if volIndex >= 10
                volIndex := 0
            if volCount < 10
                volCount += 1
            float highD = volCount > 0 ? cycleDelta / (volCount < 10 ? volCount : 10) : dLocal

            // 3) 128-bar volatility distribution + trimmed mean
            array.set(distWindow, distIndex, highD)
            distIndex += 1
            if distIndex >= 128
                distIndex := 0
            if distCount < 128
                distCount += 1

            float dRef = highD
            if distCount >= 16
                int count = distCount
                array.clear(sorted)
                for i = 0 to count - 1
                    int idx = distIndex - 1 - i
                    if idx < 0
                        idx += 128
                    array.push(sorted, array.get(distWindow, idx))
                array.sort(sorted)

                int idxLo = 0
                int idxHi = 0
                if count >= 128
                    idxLo := 32
                    idxHi := 96
                else
                    int slice = int(math.max(5.0, math.round(count * 0.5)))
                    int drop  = (count - slice) / 2
                    idxLo := drop
                    idxHi := drop + slice - 1

                if idxLo < 0
                    idxLo := 0
                if idxHi >= count
                    idxHi := count - 1

                float sum = 0.0
                for i = idxLo to idxHi
                    sum += array.get(sorted, i)
                dRef := sum / float(idxHi - idxLo + 1)

            if dRef <= 0.0
                dRef := dLocal

            // 4) Jurik dynamic exponent
            float ratio = absValue / dRef
            if ratio < 0.0
                ratio := 0.0
            float d = math.pow(ratio, _P_EXP)
            d := math.min(math.max(d, 1.0), _LOG_PARAM)

            // 5) Update UpperBand / LowerBand via sqrtDivider ^ sqrt(d)
            float adapt = math.pow(_SQRT_DIV, math.sqrt(d))
            if source > upperBand
                upperBand := source
            else
                upperBand := source - (source - upperBand) * adapt
            if source < lowerBand
                lowerBand := source
            else
                lowerBand := source - (source - lowerBand) * adapt

            // 6) 2-pole IIR core (C0/C8/A8) with Jurik alpha for middle band (JMA)
            float prevJma = na(lastJma) ? source : lastJma
            float alpha  = math.pow(_LEN_DIV, d)
            float alpha2 = alpha * alpha
            float c0 = (1.0 - alpha) * source + alpha * lastC0
            float c8 = (source - c0) * (1.0 - _LEN_DIV) + _LEN_DIV * lastC8
            float a8 = (_PHASE * c8 + c0 - prevJma) * (alpha * -2.0 + alpha2 + 1.0) + alpha2 * lastA8
            float jmaVal = prevJma + a8

            lastC0  := c0
            lastC8  := c8
            lastA8  := a8
            lastJma := jmaVal

            current_jma   := jmaVal
            current_upper := upperBand
            current_lower := lowerBand

    [current_jma, current_upper, current_lower]

// ---------- Main loop ----------

// Inputs
i_period = input.int(10, "Period", minval=1, tooltip="Number of bars used in the calculation")
i_phase  = input.int(0, "Phase", tooltip="Phase shift (-100 to 100). Negative = smoother, positive = more leading", minval=-100, maxval=100, step=10)
i_source = input.source(close, "Source")

// Calculation
[jma, upper, lower] = jbands(i_source, i_period, i_phase)

// Plot
p_upper = plot(upper, "Upper Band", color=color.new(color.red, 50), linewidth=1)
p_lower = plot(lower, "Lower Band", color=color.new(color.green, 50), linewidth=1)
plot(jma, "Middle (JMA)", color=color.yellow, linewidth=2)
fill(p_upper, p_lower, color=color.new(color.blue, 90), title="Band Fill")