mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-06 13:07:44 +00:00
Miha Kralj
107 lines
4.3 KiB
Plaintext
107 lines
4.3 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("Savitzky-Golay Moving Average (SGMA)", "SGMA", overlay=true)
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//@function Calculates SGMA using Savitzky-Golay filter with polynomial fitting
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//@param source Series to calculate SGMA from
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//@param period Lookback period - FIR window size (must be odd)
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//@param deg Polynomial degree (default: 2)
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//@returns SGMA value, calculates from first bar using available data
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//@optimized Uses Savitzky-Golay coefficients with O(n) complexity per bar due to lookback loop
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sgma(series float source, simple int period, simple int deg=2) =>
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if period <= 0
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runtime.error("Period must be greater than 0")
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int use_period = period % 2 == 0 ? period + 1 : period
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int use_deg = deg < 0 or deg >= use_period ? 2 : math.min(deg, 4)
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int p = math.min(bar_index + 1, use_period)
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var array<float> weights = array.new_float(1, 1.0)
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var int last_p = 1
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var int last_deg = use_deg
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if last_p != p or last_deg != use_deg
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weights := array.new_float(p, 0.0)
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if use_deg == 2
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if p == 5
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array.set(weights, 0, -0.0857)
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array.set(weights, 1, 0.3429)
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array.set(weights, 2, 0.4857)
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array.set(weights, 3, 0.3429)
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array.set(weights, 4, -0.0857)
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else if p == 7
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array.set(weights, 0, -0.0476)
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array.set(weights, 1, 0.0952)
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array.set(weights, 2, 0.2857)
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array.set(weights, 3, 0.3333)
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array.set(weights, 4, 0.2857)
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array.set(weights, 5, 0.0952)
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array.set(weights, 6, -0.0476)
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else if p == 9
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array.set(weights, 0, -0.0281)
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array.set(weights, 1, 0.0337)
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array.set(weights, 2, 0.1236)
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array.set(weights, 3, 0.2247)
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array.set(weights, 4, 0.2921)
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array.set(weights, 5, 0.2247)
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array.set(weights, 6, 0.1236)
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array.set(weights, 7, 0.0337)
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array.set(weights, 8, -0.0281)
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else
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float half_window = (p - 1) / 2.0
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float total_weight = 0.0
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for i = 0 to p - 1
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float x = i - half_window
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float norm_x = x / half_window
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float w = 1.0 - norm_x * norm_x
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array.set(weights, i, w)
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total_weight += w
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float inv_total = 1.0 / total_weight
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for i = 0 to p - 1
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array.set(weights, i, array.get(weights, i) * inv_total)
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else
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float half_window = (p - 1) / 2.0
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float total_weight = 0.0
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for i = 0 to p - 1
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float x = i - half_window
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float norm_x = x / half_window
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float w = 0.0
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if use_deg == 0
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w := 1.0
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else if use_deg == 1
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w := 1.0 - math.abs(norm_x)
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else if use_deg == 3
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w := 1.0 - math.abs(math.pow(norm_x, 3.0))
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else if use_deg == 4
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w := 1.0 - math.pow(norm_x, 4.0)
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else
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w := 1.0 - norm_x * norm_x
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array.set(weights, i, w)
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total_weight += w
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if total_weight > 0.0
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float inv_total = 1.0 / total_weight
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for i = 0 to p - 1
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array.set(weights, i, array.get(weights, i) * inv_total)
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last_p := p
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last_deg := use_deg
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float sum = 0.0
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float weight_sum = 0.0
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for i = 0 to p - 1
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float price = source[i]
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if not na(price)
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float w = array.get(weights, i)
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sum += price * w
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weight_sum += w
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nz(sum / weight_sum, source)
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// ---------- Main loop ----------
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// Inputs
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i_period = input.int(9, "Period", minval=3, step=2, tooltip="Must be odd number (will be adjusted if even)")
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i_degree = input.int(2, "Polynomial Degree", minval=0, maxval=4, tooltip="Higher degrees fit more complex shapes but risk overfitting")
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i_source = input.source(close, "Source")
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// Calculation
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sgma_value = sgma(i_source, i_period, i_degree)
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// Plot
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plot(sgma_value, "SGMA", color=color.yellow, linewidth=2)
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