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https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
88 lines
2.9 KiB
Plaintext
88 lines
2.9 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("Nyquist Moving Average (NYQMA)", "NYQMA", overlay=true)
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//@function Nyquist Moving Average per Dr. Manfred G. Dürschner ("Gleitende Durchschnitte 3.0").
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// Applies the Nyquist-Shannon sampling theorem to cascaded LWMAs: a single-smoothed
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// LWMA and a double-smoothed LWMA are combined via lag-compensating extrapolation.
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// Formula: NYQMA = (1 + α) · MA1 − α · MA2, where α = N2 / (N1 − N2).
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// The second LWMA period (N2) must satisfy N2 ≤ floor(N1/2) per Nyquist criterion
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// to prevent aliasing artifacts ("ghost signals") in the smoothed output.
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//@param source Series to smooth
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//@param period Primary LWMA period (N1), must be ≥ 3
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//@param nyquist_period Secondary LWMA period (N2), clamped to ≤ floor(N1/2)
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//@returns Nyquist-compliant lag-compensated moving average
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nyqma(series float source, simple int period, simple int nyquist_period) =>
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if period < 3
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runtime.error("Period must be at least 3")
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float price = nz(source)
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int n2 = math.min(math.max(nyquist_period, 1), period / 2)
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// ── MA1: LWMA(source, period) with O(1) circular buffer ──
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var array<float> buf1 = array.new_float(period, na)
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var int head1 = 0
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var float sum1 = 0.0
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var float wsum1 = 0.0
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var int cnt1 = 0
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float oldest1 = array.get(buf1, head1)
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if not na(oldest1)
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float old_sum1 = sum1
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sum1 -= oldest1
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sum1 += price
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wsum1 := wsum1 - old_sum1 + period * price
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else
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cnt1 += 1
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sum1 += price
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wsum1 := wsum1 + cnt1 * price
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array.set(buf1, head1, price)
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head1 := (head1 + 1) % period
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int p1 = math.min(cnt1, period)
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float norm1 = p1 * (p1 + 1) * 0.5
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float ma1 = wsum1 / norm1
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// ── MA2: LWMA(MA1, n2) with O(1) circular buffer ──
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var array<float> buf2 = array.new_float(n2, na)
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var int head2 = 0
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var float sum2 = 0.0
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var float wsum2 = 0.0
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var int cnt2 = 0
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float oldest2 = array.get(buf2, head2)
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if not na(oldest2)
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float old_sum2 = sum2
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sum2 -= oldest2
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sum2 += ma1
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wsum2 := wsum2 - old_sum2 + n2 * ma1
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else
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cnt2 += 1
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sum2 += ma1
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wsum2 := wsum2 + cnt2 * ma1
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array.set(buf2, head2, ma1)
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head2 := (head2 + 1) % n2
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int p2 = math.min(cnt2, n2)
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float norm2 = p2 * (p2 + 1) * 0.5
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float ma2 = wsum2 / norm2
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// ── Lag-compensating extrapolation ──
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float alpha = float(n2) / float(period - n2)
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float result = (1.0 + alpha) * ma1 - alpha * ma2
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result
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// ── Inputs ──
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int p_period = input.int(89, "Period (N1)", minval=3)
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int p_nyquist = input.int(21, "Nyquist Period (N2)", minval=1)
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float p_src = input.source(close, "Source")
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// ── Calculation ──
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float out = nyqma(p_src, p_period, p_nyquist)
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// ── Plot ──
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plot(out, "NYQMA", color.yellow, 2)
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