Squeeze Momentum

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Squeeze Momentum (SQUEEZE)", "SQUEEZE", overlay=false)

//@function Calculates Squeeze Momentum — BB vs KC squeeze detection with LinReg momentum
//@param source Series to evaluate (typically close)
//@param period Lookback period for BB, KC, Donchian midline, and LinReg
//@param bbMult Bollinger Band standard deviation multiplier
//@param kcMult Keltner Channel ATR multiplier
//@returns [momentum, squeezeOn] momentum histogram and squeeze state (1=on, 0=off)
//@description Squeeze Momentum detects low-volatility compressions (BB inside KC)
//  and measures directional momentum via linear regression:
//    Bollinger Bands: SMA ± bbMult × StdDev(period)
//    Keltner Channel: EMA ± kcMult × ATR(period) using Wilder RMA
//    Squeeze On: BB_upper < KC_upper and BB_lower > KC_lower
//    Midline: (Highest(high, period) + Lowest(low, period)) / 2
//    Delta: close - (midline + SMA) / 2
//    Momentum: LinReg(delta, period) evaluated at endpoint
//  SMA and variance use O(1) circular buffer (§3 warmup).
//  EMA and RMA use §2 exponential warmup compensators.
//  Donchian highest/lowest use circular buffers with running max/min scan.
//  LinReg uses incremental O(1) running sums (ΣY, ΣXY).
//  Positive momentum = bullish, negative = bearish.
//  Squeeze transitions (on→off) signal potential breakout moves.
squeeze(series float source, simple int period, simple float bbMult, simple float kcMult) =>
    if period <= 0
        runtime.error("Period must be greater than 0")
    if bbMult <= 0.0
        runtime.error("BB multiplier must be greater than 0")
    if kcMult <= 0.0
        runtime.error("KC multiplier must be greater than 0")

    float EPSILON = 1e-10

    // ===== SMA + Variance (circular buffer, §3 warmup) =====
    var array<float> smaBuf = array.new_float(period, na)
    var int smaHead         = 0
    var float smaSum        = 0.0
    var float smaSumSq      = 0.0
    var int smaCount        = 0

    float srcVal = nz(source)
    float oldSma = array.get(smaBuf, smaHead)
    if not na(oldSma)
        smaSum   -= oldSma
        smaSumSq -= oldSma * oldSma
    else
        smaCount += 1
    smaSum   += srcVal
    smaSumSq += srcVal * srcVal
    array.set(smaBuf, smaHead, srcVal)
    smaHead := (smaHead + 1) % period

    int n = math.max(1, smaCount)
    float smaVal  = smaSum / float(n)
    float variance = math.max(0.0, smaSumSq / float(n) - smaVal * smaVal)
    float stddev   = math.sqrt(variance)

    float bbUpper = smaVal + bbMult * stddev
    float bbLower = smaVal - bbMult * stddev

    // ===== EMA for KC midline (§2 warmup) =====
    var float rawEma = 0.0
    var float eEma   = 1.0
    float emaAlpha   = 2.0 / (float(period) + 1.0)
    float emaBeta    = 1.0 - emaAlpha

    rawEma := rawEma * emaBeta + srcVal * emaAlpha
    eEma *= emaBeta
    float cEma = eEma > EPSILON ? 1.0 / (1.0 - eEma) : 1.0
    float emaVal = rawEma * cEma

    // ===== True Range + RMA for ATR (§2 warmup) =====
    var float prevClose = na
    float trueRange = high - low
    if not na(prevClose)
        trueRange := math.max(trueRange, math.max(math.abs(high - prevClose), math.abs(low - prevClose)))
    prevClose := close

    var float rawRma = 0.0
    var float eRma   = 1.0
    float rmaAlpha   = 1.0 / float(period)
    float rmaBeta    = 1.0 - rmaAlpha

    rawRma := rawRma * rmaBeta + trueRange * rmaAlpha
    eRma *= rmaBeta
    float cRma = eRma > EPSILON ? 1.0 / (1.0 - eRma) : 1.0
    float atr = rawRma * cRma

    float kcUpper = emaVal + kcMult * atr
    float kcLower = emaVal - kcMult * atr

    // ===== Squeeze detection =====
    float sqOn = bbUpper < kcUpper and bbLower > kcLower ? 1.0 : 0.0

    // ===== Donchian midline: (highest + lowest) / 2 over period =====
    var array<float> hiBuf = array.new_float(period, na)
    var array<float> loBuf = array.new_float(period, na)
    var int donHead        = 0

    array.set(hiBuf, donHead, high)
    array.set(loBuf, donHead, low)
    donHead := (donHead + 1) % period

    float highest = high
    float lowest  = low
    for i = 0 to period - 1
        float h = array.get(hiBuf, i)
        float l = array.get(loBuf, i)
        if not na(h)
            highest := math.max(highest, h)
        if not na(l)
            lowest := math.min(lowest, l)

    float donMid = (highest + lowest) / 2.0

    // ===== Delta: close - average of donchian midline and SMA =====
    float delta = srcVal - (donMid + smaVal) / 2.0

    // ===== LinReg of delta over period (O(1) incremental) =====
    var array<float> lrBuf = array.new_float(period, na)
    var int lrHead         = 0
    var float sumY         = 0.0
    var float sumXY        = 0.0
    var int lrCount        = 0

    float oldLr = array.get(lrBuf, lrHead)
    if not na(oldLr)
        int oldIdx = lrCount - period
        sumY  -= oldLr
        sumXY -= float(oldIdx) * oldLr
    else
        // noop — count handles warmup
        nop = 0

    sumY  += delta
    sumXY += float(lrCount) * delta
    array.set(lrBuf, lrHead, delta)
    lrHead := (lrHead + 1) % period

    lrCount += 1

    int pn = math.min(lrCount, period)
    int startIdx = lrCount - pn
    float sumX   = float(pn) * float(startIdx + startIdx + pn - 1) / 2.0
    float sumX2  = 0.0
    for i = 0 to pn - 1
        float xi = float(startIdx + i)
        sumX2 += xi * xi

    float denomX = float(pn) * sumX2 - sumX * sumX
    float slope  = denomX == 0.0 ? 0.0 : (float(pn) * sumXY - sumX * sumY) / denomX
    float intercept = (sumY - slope * sumX) / float(pn)
    float momentum  = slope * float(lrCount - 1) + intercept

    [momentum, sqOn]

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

// Inputs
i_source = input.source(close, "Source")
i_period = input.int(20, "Period", minval=1)
i_bbMult = input.float(2.0, "BB Multiplier", minval=0.001, step=0.1)
i_kcMult = input.float(1.5, "KC Multiplier", minval=0.001, step=0.1)

// Calculation
[mom, sqOn] = squeeze(i_source, i_period, i_bbMult, i_kcMult)

// Plot
momColor = mom > 0 ? (mom > nz(mom[1]) ? color.lime : color.green) : (mom < nz(mom[1]) ? color.red : color.maroon)
plot(mom, "Momentum", color=momColor, linewidth=2, style=plot.style_histogram)
plot(sqOn == 1.0 ? 0 : na, "Squeeze On", color=color.red, linewidth=4, style=plot.style_circles)
plot(sqOn == 0.0 ? 0 : na, "Squeeze Off", color=color.lime, linewidth=4, style=plot.style_circles)
hline(0, "Zero", color=color.gray, linestyle=hline.style_dotted)