mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-03 03:47:42 +00:00
Miha Kralj
93 lines
2.7 KiB
Plaintext
93 lines
2.7 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("HEMA (Exponential Hull Analog)", "HEMAx", overlay=true)
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//@function Calculates Hull Exponential Moving Average (EMA-domain HMA analog)
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//@param src Series to calculate HEMA from
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//@param N Period (matches HMA lag at same period)
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//@returns HEMA value with reduced lag
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//@optimized Uses cascaded EMA de-lag structure with O(1) complexity per bar
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// WMA-lag-matched alpha: EMA lag = (P-1)/3, same as WMA(P)
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alphaFromWmaLag(int p) =>
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float fp = math.max(float(p), 1.0)
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3.0 / (fp + 2.0)
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// Exponential Hull Analog (EMA-domain HMA)
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hema(series float src, simple int N) =>
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// --- guardrails ---
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int n = math.max(N, 2) // HMA-like structure needs N>=2
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// --- sub-periods matching HMA's integer floor divisions ---
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int halfN = int(n / 2) // floor(N/2), same as HMA
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int sqrtN = math.max(int(math.sqrt(n)), 1) // floor(sqrt(N)), same as HMA
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// --- alphas (lag-matched to WMA) ---
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float aS = alphaFromWmaLag(n)
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float aF = alphaFromWmaLag(math.max(halfN, 1))
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float aM = alphaFromWmaLag(math.max(sqrtN, 1))
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float bS = 1.0 - aS
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float bF = 1.0 - aF
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float bM = 1.0 - aM
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// --- lag-derived ratio for the de-lag combiner ---
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float lagS = bS / aS
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float lagF = bF / aF
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float r = lagF / lagS
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r := math.min(math.max(r, 0.0), 0.999999) // keep denom sane
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// --- state (unbiased EMA warmup) ---
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var bool warmup = true
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var float dS = 1.0
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var float dF = 1.0
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var float dM = 1.0
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var float eSraw = 0.0
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var float eFraw = 0.0
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var float eMraw = 0.0
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float eS = na
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float eF = na
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float out = na
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// raw EMAs
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eSraw := aS * (src - eSraw) + eSraw
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eFraw := aF * (src - eFraw) + eFraw
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if warmup
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// update decays for unbiased correction
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dS *= bS
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dF *= bF
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dM *= bM
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float invS = 1.0 / math.max(1.0 - dS, 1e-12)
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float invF = 1.0 / math.max(1.0 - dF, 1e-12)
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float invM = 1.0 / math.max(1.0 - dM, 1e-12)
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eS := eSraw * invS
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eF := eFraw * invF
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float deLag = (eF - r * eS) / (1.0 - r)
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eMraw := aM * (deLag - eMraw) + eMraw
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out := eMraw * invM
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// end warmup only when ALL stages are effectively unbiased
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warmup := math.max(dS, math.max(dF, dM)) > 1e-10
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else
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eS := eSraw
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eF := eFraw
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float deLag = (eF - r * eS) / (1.0 - r)
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eMraw := aM * (deLag - eMraw) + eMraw
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out := eMraw
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out
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// Inputs
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i_period = input.int(10, "Period", minval=2)
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i_source = input.source(close, "Source")
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hema_value = hema(i_source, i_period)
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plot(hema_value, "HEMA", color=color.yellow, linewidth=2)
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