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https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
92 lines
3.1 KiB
Plaintext
92 lines
3.1 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 algorithm (C) 2004-2024 John F. Ehlers
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indicator("Ehlers Predictive Moving Average (PMA)", "PMA", overlay=true)
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//@function Calculates Ehlers Predictive Moving Average using WMA-based linear extrapolation
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//@param source Series to calculate PMA from
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//@param period Lookback period for WMA smoothing (>= 1, default 7 per Ehlers)
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//@returns [pma, trigger] where PMA = 2×WMA − WMA(WMA) and Trigger = (4×WMA − WMA(WMA)) / 3
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//@optimized Uses dual running sums with cached denominator for O(1) WMA complexity per bar
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pma(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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// --- First WMA: WMA(source, period) --- matches canonical wma.pine pattern
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var array<float> buffer1 = 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 weighted_sum1 = 0.0
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var int count1 = 0
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var float norm1 = 0.0
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float oldest1 = array.get(buffer1, head1)
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float current1 = nz(source)
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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 += current1
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weighted_sum1 := weighted_sum1 - old_sum1 + (period * current1)
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else
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count1 += 1
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sum1 += current1
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weighted_sum1 := weighted_sum1 + (count1 * current1)
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norm1 := count1 * (count1 + 1) * 0.5
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array.set(buffer1, head1, current1)
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head1 := (head1 + 1) % period
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float wma1 = weighted_sum1 / norm1
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// --- Second WMA: WMA(WMA1, period) --- same O(1) circular buffer on first WMA output
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var array<float> buffer2 = array.new_float(period, na)
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var int head2 = 0
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var float sum2 = 0.0
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var float weighted_sum2 = 0.0
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var int count2 = 0
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var float norm2 = 0.0
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float oldest2 = array.get(buffer2, head2)
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float current2 = nz(wma1)
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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 += current2
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weighted_sum2 := weighted_sum2 - old_sum2 + (period * current2)
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else
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count2 += 1
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sum2 += current2
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weighted_sum2 := weighted_sum2 + (count2 * current2)
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norm2 := count2 * (count2 + 1) * 0.5
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array.set(buffer2, head2, current2)
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head2 := (head2 + 1) % period
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float wma2 = weighted_sum2 / norm2
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// Predictive line: cancels one WMA lag via linear extrapolation
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// PMA = 2 × WMA(src) − WMA(WMA(src))
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float pma_val = 2.0 * wma1 - wma2
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// Trigger/signal line: weighted blend for crossover signals
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// Trigger = (4 × WMA(src) − WMA(WMA(src))) / 3
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float trigger_val = (4.0 * wma1 - wma2) / 3.0
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[na(source) ? na : pma_val, na(source) ? na : trigger_val]
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// ---------- Main loop ----------
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// Inputs
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i_period = input.int(7, "Period", minval=1, tooltip="Lookback period for WMA smoothing (Ehlers default: 7)")
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i_source = input.source(close, "Source")
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// Calculation
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[pma_value, trigger_value] = pma(i_source, i_period)
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// Plot
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plot(pma_value, "PMA", color=color.yellow, linewidth=2)
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plot(trigger_value, "Trigger", color=color.orange, linewidth=1)
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