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Miha Kralj
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// The MIT License (MIT)
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// © mihakralj
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//@version=6
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indicator("Jurik Adaptive Envelope Bands", "JBANDS", overlay=true)
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//@function Jurik Adaptive Envelope Bands - Upper/Lower bands from JMA's adaptive envelope tracking
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//@doc Bands snap to new extremes instantly but decay smoothly toward price,
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//@doc creating volatility-responsive channels with JMA's signature smoothness.
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//@param source Series to calculate JBANDS from
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//@param period Number of bars used in the calculation (>= 1)
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//@param phase Phase shift (-100 to 100). Negative = smoother, positive = more leading
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//@returns Array of [middle (JMA), upper, lower]
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jbands(series float source, simple int period, simple int phase = 0) =>
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// ---- Precomputed length/phase parameters (constant per series) ----
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simple float _PHASE = phase < -100 ? 0.5 : phase > 100 ? 2.5 : (phase * 0.01) + 1.5
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simple float _LEN0 = period < 1.0000000002 ? 1e-10 : (period - 1.0) / 2.0
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simple float _LOG_PARAM = math.max(math.log(math.sqrt(_LEN0)) / math.log(2.0) + 2.0, 0.0)
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simple float _SQRT_PARAM = math.sqrt(_LEN0) * _LOG_PARAM
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simple float _LEN_ADJ = _LEN0 * 0.9
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simple float _LEN_DIV = _LEN_ADJ / (_LEN_ADJ + 2.0)
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simple float _SQRT_DIV = _SQRT_PARAM / (_SQRT_PARAM + 1.0)
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simple float _P_EXP = math.max(_LOG_PARAM - 2.0, 0.5)
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// ---- Internal state (persists across bars) ----
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var float upperBand = na
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var float lowerBand = na
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var float lastC0 = na
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var float lastC8 = na
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var float lastA8 = na
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var float lastJma = na
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var int bars = 0
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// 10-bar local deviation window
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var float cycleDelta = 0.0
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var int volIndex = 0
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var int volCount = 0
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var array<float> volWindow = array.new_float(10, 0.0)
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// 128-bar volatility distribution
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var int distIndex = 0
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var int distCount = 0
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var array<float> distWindow = array.new_float(128, 0.0)
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var array<float> sorted = array.new_float(0)
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float current_jma = na
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float current_upper = na
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float current_lower = na
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if not na(source)
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bars += 1
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// ---- First bar: initialize anchors and filter state ----
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if bars == 1
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upperBand := source
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lowerBand := source
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lastC0 := source
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lastC8 := 0.0
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lastA8 := 0.0
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lastJma := source
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current_jma := source
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current_upper := source
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current_lower := source
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else
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// 1) Local deviation vs. UpperBand / LowerBand
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float diffA = source - upperBand
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float diffB = source - lowerBand
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float absA = math.abs(diffA)
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float absB = math.abs(diffB)
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float absValue = absA > absB ? absA : absB
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float dLocal = absValue + 1e-10
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// 2) 10-bar SMA of local deviation -> highD
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float oldVol = array.get(volWindow, volIndex)
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cycleDelta += dLocal - oldVol
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array.set(volWindow, volIndex, dLocal)
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volIndex += 1
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if volIndex >= 10
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volIndex := 0
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if volCount < 10
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volCount += 1
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float highD = volCount > 0 ? cycleDelta / (volCount < 10 ? volCount : 10) : dLocal
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// 3) 128-bar volatility distribution + trimmed mean
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array.set(distWindow, distIndex, highD)
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distIndex += 1
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if distIndex >= 128
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distIndex := 0
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if distCount < 128
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distCount += 1
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float dRef = highD
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if distCount >= 16
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int count = distCount
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array.clear(sorted)
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for i = 0 to count - 1
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int idx = distIndex - 1 - i
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if idx < 0
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idx += 128
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array.push(sorted, array.get(distWindow, idx))
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array.sort(sorted)
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int idxLo = 0
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int idxHi = 0
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if count >= 128
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idxLo := 32
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idxHi := 96
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else
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int slice = int(math.max(5.0, math.round(count * 0.5)))
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int drop = (count - slice) / 2
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idxLo := drop
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idxHi := drop + slice - 1
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if idxLo < 0
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idxLo := 0
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if idxHi >= count
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idxHi := count - 1
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float sum = 0.0
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for i = idxLo to idxHi
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sum += array.get(sorted, i)
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dRef := sum / float(idxHi - idxLo + 1)
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if dRef <= 0.0
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dRef := dLocal
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// 4) Jurik dynamic exponent
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float ratio = absValue / dRef
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if ratio < 0.0
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ratio := 0.0
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float d = math.pow(ratio, _P_EXP)
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d := math.min(math.max(d, 1.0), _LOG_PARAM)
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// 5) Update UpperBand / LowerBand via sqrtDivider ^ sqrt(d)
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float adapt = math.pow(_SQRT_DIV, math.sqrt(d))
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if source > upperBand
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upperBand := source
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else
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upperBand := source - (source - upperBand) * adapt
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if source < lowerBand
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lowerBand := source
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else
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lowerBand := source - (source - lowerBand) * adapt
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// 6) 2-pole IIR core (C0/C8/A8) with Jurik alpha for middle band (JMA)
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float prevJma = na(lastJma) ? source : lastJma
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float alpha = math.pow(_LEN_DIV, d)
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float alpha2 = alpha * alpha
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float c0 = (1.0 - alpha) * source + alpha * lastC0
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float c8 = (source - c0) * (1.0 - _LEN_DIV) + _LEN_DIV * lastC8
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float a8 = (_PHASE * c8 + c0 - prevJma) * (alpha * -2.0 + alpha2 + 1.0) + alpha2 * lastA8
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float jmaVal = prevJma + a8
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lastC0 := c0
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lastC8 := c8
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lastA8 := a8
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lastJma := jmaVal
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current_jma := jmaVal
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current_upper := upperBand
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current_lower := lowerBand
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[current_jma, current_upper, current_lower]
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// ---------- Main loop ----------
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// Inputs
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i_period = input.int(10, "Period", minval=1, tooltip="Number of bars used in the calculation")
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i_phase = input.int(0, "Phase", tooltip="Phase shift (-100 to 100). Negative = smoother, positive = more leading", minval=-100, maxval=100, step=10)
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i_source = input.source(close, "Source")
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// Calculation
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[jma, upper, lower] = jbands(i_source, i_period, i_phase)
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// Plot
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p_upper = plot(upper, "Upper Band", color=color.new(color.red, 50), linewidth=1)
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p_lower = plot(lower, "Lower Band", color=color.new(color.green, 50), linewidth=1)
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plot(jma, "Middle (JMA)", color=color.yellow, linewidth=2)
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fill(p_upper, p_lower, color=color.new(color.blue, 90), title="Band Fill")
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