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https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
77 lines
3.0 KiB
Plaintext
77 lines
3.0 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("Parzen Window Moving Average (PARZEN)", "PARZEN", overlay=true)
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//@function Computes Parzen (de la Vallée-Poussin) Window Moving Average — a symmetric
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// FIR filter using the Parzen window function. The Parzen window is a piecewise
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// cubic polynomial with zero sidelobe discontinuity, giving excellent sidelobe
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// suppression (-24 dB/octave rolloff). It is the convolution of two triangular
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// (Bartlett) windows at half-length, producing a smooth bell-shaped kernel.
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// w(k) = 1 - 6u² + 6|u|³ for |u| ≤ 0.5
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// w(k) = 2(1 - |u|)³ for 0.5 < |u| ≤ 1.0
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// where u = 2k/(N-1) normalized to [-1,1] center-symmetric.
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//@param source Series to smooth
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//@param period Lookback window (>= 2)
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//@returns Parzen-weighted moving average
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//@reference Parzen, E. (1961). "Mathematical Considerations in the Estimation of Spectra."
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// Technometrics, 3(2), 167–190.
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//@optimized O(period) per bar for convolution; weights precomputed once
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parzen(series float source, simple int period) =>
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if period < 2
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runtime.error("Period must be at least 2")
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float price = nz(source)
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// --- Circular buffer for rolling window ---
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var array<float> buffer = array.new_float(period, na)
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var int head = 0
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array.set(buffer, head, price)
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head := (head + 1) % period
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// --- Precompute Parzen window weights once ---
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var array<float> weights = array.new_float(0)
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if barstate.isfirst
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float half_N = (period - 1) / 2.0
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float wsum = 0.0
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for k = 0 to period - 1
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// u normalized to [-1, 1] centered on the middle of the window
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float u = half_N > 0 ? (k - half_N) / half_N : 0.0
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float abs_u = math.abs(u)
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float w = 0.0
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if abs_u <= 0.5
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// Inner region: cubic spline
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w := 1.0 - 6.0 * abs_u * abs_u + 6.0 * abs_u * abs_u * abs_u
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else if abs_u <= 1.0
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// Outer region: cubic taper to zero
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float t = 1.0 - abs_u
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w := 2.0 * t * t * t
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array.push(weights, w)
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wsum += w
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// Normalize weights to sum exactly 1.0
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if wsum > 0
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for j = 0 to period - 1
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array.set(weights, j, array.get(weights, j) / wsum)
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int count = math.min(bar_index + 1, period)
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if count < period
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price
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else
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// --- Apply Parzen window convolution via circular buffer ---
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// Buffer: head points to next-write = oldest entry
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// Weight[0] = oldest bar, Weight[period-1] = newest
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float result = 0.0
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for j = 0 to period - 1
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int idx = (head + j) % period
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float val = nz(array.get(buffer, idx))
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result += val * array.get(weights, j)
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result
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// ── Inputs ──
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src = input.source(close, "Source")
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per = input.int(14, "Period", minval = 2)
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// ── Plot ──
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plot(parzen(src, per), "PARZEN", color.yellow, 2)
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