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46 lines
1.8 KiB
Plaintext
46 lines
1.8 KiB
Plaintext
// The MIT License (MIT)
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// © mihakralj
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//@version=6
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indicator("Ahrens Moving Average (AHRENS)", "AHRENS", overlay=true)
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//@function Calculates Ahrens Moving Average using midpoint correction between current and lagged MA values
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//@param source Series to smooth
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//@param period Lookback length for the lag component and smoothing divisor
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//@returns Ahrens MA value — a recursive IIR filter that adjusts toward source minus the midpoint of its current and lagged states
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//@algorithm ahma = ahma[1] + (source - (ahma[1] + ahma[period]) / 2) / period
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//@reference Richard D. Ahrens, "Build A Better Moving Average" (Stocks & Commodities V.31:11, October 2013)
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//@optimized O(1) per bar via circular buffer for lagged MA state; O(period) memory for the ring buffer
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ahrens(series float source, simple int period) =>
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if period <= 0
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runtime.error("Period must be greater than 0")
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// Circular buffer to store past ahma values for period-bar lookback
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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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var float result = na
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if not na(source)
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float prev = nz(result, source)
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float lagged = nz(array.get(buffer, head), source)
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// Ahrens formula: ahma = prev + (source - midpoint(prev, lagged)) / period
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float midpoint = (prev + lagged) * 0.5
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result := prev + (source - midpoint) / float(period)
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// Store current result in circular buffer and advance head
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array.set(buffer, head, result)
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head := (head + 1) % period
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result
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// ---------- Main loop ----------
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// Inputs
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i_period = input.int(9, "Period", minval=1)
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i_source = input.source(close, "Source")
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// Calculation
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ahrens_value = ahrens(i_source, i_period)
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// Plot
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plot(ahrens_value, "AHRENS", color=color.yellow, linewidth=2)
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