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https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
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- Updated BBWN, BBWP, CCV, CV, CVI, EWMA, GKV, HLV, HV, Jvolty, JVOLTYN, MASSI, NATR, RSV, RV, RVI, TR, UI, VOV, VR, YZV indicators with documentation links. - Added documentation links for Aberration, Acceleration Bands, Andrews' Pitchfork, Adaptive Price Zone, ATR Bands, Bollinger Bands, Center of Gravity, Donchian Channels, Decay Min-Max Channel, Detrended Synthetic Price, EACP, EBSW, HOMOD, Jurik Volatility Bands, Keltner Channel, MA Envelope, Min-Max Channel, Price Channel, Regression Channels, Standard Deviation Channel, Stoller Average Range Channel, Super Trend Bands, Ultimate Bands, Ultimate Channel, VWAP Bands, and VWAP with Standard Deviation Bands.
146 lines
3.7 KiB
Plaintext
146 lines
3.7 KiB
Plaintext
// The MIT License (MIT)
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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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