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https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
84 lines
3.7 KiB
Plaintext
84 lines
3.7 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("Kaiser Window Moving Average (KAISER)", "KAISER", overlay=true)
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//@function I0 approximation (modified Bessel, first kind, order 0) via 25-term power series.
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bessel_i0(float x) =>
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float sum = 1.0
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float term = 1.0
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float half_x = x / 2.0
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for m = 1 to 25
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term *= (half_x / m)
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sum += term * term
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sum
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//@function Computes Kaiser Window Moving Average — a symmetric FIR filter using the
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// Kaiser-Bessel window function for optimal sidelobe attenuation. The beta
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// parameter controls the trade-off between main lobe width and sidelobe level.
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//@param source Series to smooth
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//@param period Lookback window (>= 2)
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//@param beta Kaiser shape parameter controlling sidelobe attenuation (default 3.0).
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// Higher beta = smoother (more attenuation) but wider transition band.
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// beta=0 reduces to rectangular (SMA), beta~5.65 approximates Blackman.
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//@returns Kaiser-weighted moving average
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//@reference Kaiser, J.F. & Schafer, R.W. (1980). "On the Use of the I0-Sinh Window
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// for Spectrum Analysis." IEEE Trans. Acoust., Speech, Signal Process.
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//@optimized O(period) per bar for convolution; weights precomputed once via I0 series
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kaiser(series float source, simple int period, simple float beta = 3.0) =>
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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 Kaiser window weights once ---
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// Kaiser window: w(k) = I0(beta * sqrt(1 - ((2k/(N-1)) - 1)^2)) / I0(beta)
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var array<float> weights = array.new_float(0)
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if barstate.isfirst
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float i0_beta = bessel_i0(beta)
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float N = period - 1
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float wsum = 0.0
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for k = 0 to period - 1
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float t = N > 0 ? (2.0 * k / N) - 1.0 : 0.0
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float arg_sq = 1.0 - t * t
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// Clamp to avoid sqrt of negative due to floating-point
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float arg = arg_sq > 0 ? math.sqrt(arg_sq) : 0.0
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float w = i0_beta > 0 ? bessel_i0(beta * arg) / i0_beta : 1.0
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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 Kaiser 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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bet = input.float(3.0, "Beta (shape)", minval=0, maxval=20, step=0.1,
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tooltip="0=rectangular(SMA), 3=good general, 5.65≈Blackman, 8.6=Hamming-like")
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// ── Plot ────────────────────────────────────────────────────────────────
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plot(kaiser(src, per, bet), "KAISER", color.new(color.yellow, 0), 2)
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