mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-07-27 17:27:43 +00:00
Miha Kralj
146 lines
3.8 KiB
Plaintext
146 lines
3.8 KiB
Plaintext
// Licensed under the Apache License, Version 2.0
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// © mihakralj
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//@version=6
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indicator("QEMA (OptA, progressive α, period-only)", "QEMA OptA", overlay=true)
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//@function Calculates Quad EMA with progressive alphas and Option A zero-lag weights
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//@param srcIn Series to calculate QEMA from
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//@param period Lookback period for alpha calculation (>= 1)
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//@returns QEMA value with minimized DC lag
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//@optimized Uses 4-stage cascaded EMA with optimal weights, O(1) complexity per bar
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// ---------- Inputs ----------
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i_period = input.int(15, "Period", minval=1)
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i_source = input.source(close, "Source")
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// ---------- Helpers ----------
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clamp01(x) =>
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math.min(1.0, math.max(x, 1e-12))
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lag(alpha) =>
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(1.0 - alpha) / alpha
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// ---------- QEMA: progressive alphas + Option A weights ----------
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qema_optA(series float srcIn, int period) =>
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// --- dirty-data guard (NA only; Pine doesn't expose isfinite/isinf) ---
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var float lastFinite = na
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float src = srcIn
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if na(src)
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src := nz(lastFinite, src)
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else
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lastFinite := src
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// --- base alpha from period ---
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float a1 = clamp01(2.0 / (period + 1.0))
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// --- progressive alpha ramp (your design) ---
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// r = (1/a1)^(1/4) -> a2=a1^(3/4), a3=a1^(1/2), a4=a1^(1/4)
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float r = math.pow(1.0 / a1, 0.25)
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float a2 = clamp01(a1 * r)
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float a3 = clamp01(a2 * r)
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float a4 = clamp01(a3 * r)
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float d1 = 1.0 - a1
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float d2 = 1.0 - a2
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float d3 = 1.0 - a3
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float d4 = 1.0 - a4
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// --- unbiased warmup (startup bias compensation) ---
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var float e1 = 1.0
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var float e2 = 1.0
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var float e3 = 1.0
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var float e4 = 1.0
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var bool warmup = true
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// --- EMA accumulators ---
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var float rema1 = 0.0
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var float rema2 = 0.0
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var float rema3 = 0.0
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var float rema4 = 0.0
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float ema1 = na
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float ema2 = na
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float ema3 = na
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float ema4 = na
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// Stage 1
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rema1 := rema1 + a1 * (src - rema1)
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if warmup
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e1 *= d1
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e2 *= d2
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e3 *= d3
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e4 *= d4
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float c1 = 1.0 / (1.0 - e1)
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float c2 = 1.0 / (1.0 - e2)
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float c3 = 1.0 / (1.0 - e3)
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float c4 = 1.0 / (1.0 - e4)
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ema1 := rema1 * c1
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rema2 := rema2 + a2 * (ema1 - rema2)
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ema2 := rema2 * c2
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rema3 := rema3 + a3 * (ema2 - rema3)
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ema3 := rema3 * c3
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rema4 := rema4 + a4 * (ema3 - rema4)
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ema4 := rema4 * c4
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// stage 1 is slowest => if it's unbiased, others are too
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warmup := e1 > 1e-10
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else
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ema1 := rema1
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rema2 := rema2 + a2 * (ema1 - rema2)
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ema2 := rema2
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rema3 := rema3 + a3 * (ema2 - rema3)
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ema3 := rema3
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rema4 := rema4 + a4 * (ema3 - rema4)
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ema4 := rema4
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// --- cumulative lags (mean-lag proxy) ---
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float t1 = lag(a1)
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float t2 = lag(a2)
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float t3 = lag(a3)
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float t4 = lag(a4)
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float L1 = t1
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float L2 = t1 + t2
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float L3 = L2 + t3
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float L4 = L3 + t4
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// --- Option A weights: min-energy with constraints ---
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// Σw = 1
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// Σw*L = δ, with δ=0 here (zero DC lag)
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float delta = 0.0
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float B = L1 + L2 + L3 + L4
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float C = L1*L1 + L2*L2 + L3*L3 + L4*L4
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float D = 4.0*C - B*B
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float w1 = na
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float w2 = na
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float w3 = na
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float w4 = na
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if math.abs(D) < 1e-12
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// degenerate (e.g. a1==1 -> all L=0): safest output is ema1==src
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w1 := 1.0
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w2 := 0.0
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w3 := 0.0
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w4 := 0.0
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else
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float lambda = (C - B*delta) / D
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float mu = (-B + 4.0*delta) / D
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w1 := lambda + mu*L1
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w2 := lambda + mu*L2
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w3 := lambda + mu*L3
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w4 := lambda + mu*L4
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w1*ema1 + w2*ema2 + w3*ema3 + w4*ema4
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// ---------- Main ----------
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float q = qema_optA(i_source, i_period)
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plot(q, "QEMA OptA", color.new(color.yellow, 0), 2)
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