mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-02 03:37:42 +00:00
Miha Kralj
91 lines
3.3 KiB
Plaintext
91 lines
3.3 KiB
Plaintext
// This Pine Script™ code is subject to the terms of the Mozilla Public License 2.0
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// https://mozilla.org/MPL/2.0/
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// © QuanTAlib
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//@version=6
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indicator("Ehlers Reflex Indicator (REFLEX)", "REFLEX", overlay = false)
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//@function Ehlers Reflex — a zero-lag oscillator that measures the reflex (reversal
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// tendency) of price by comparing the SSF-filtered price against a linear
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// extrapolation from N bars ago. Applies a 2-pole Super Smoother pre-filter
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// at half the specified period, then computes slope = (Filt[N] - Filt) / N,
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// sums deviations of the extrapolated line from actual filtered values over
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// the window, and normalizes by exponential RMS. Values above 0 suggest
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// uptrend, below 0 suggest downtrend; crossovers signal reversals.
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//@param source Series to analyze
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//@param period Lookback window / assumed cycle period (>= 2)
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//@returns Reflex oscillator value (normalized, roughly ±σ scale)
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//@reference Ehlers, J.F. (2020). "Reflex: A New Zero-Lag Indicator."
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// Technical Analysis of Stocks & Commodities, Feb 2020.
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//@optimized O(period) per bar for the summation loop; SSF is O(1) IIR
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reflex(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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// --- 2-Pole Super Smoother Filter (half-period cutoff) ---
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float half_period = period * 0.5
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float a1 = math.exp(-1.414 * math.pi / half_period)
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float b1 = 2.0 * a1 * math.cos(1.414 * math.pi / half_period)
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float c2 = b1
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float c3 = -(a1 * a1)
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float c1 = 1.0 - c2 - c3
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var float filt = 0.0
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var float filt1 = 0.0
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var float filt2 = 0.0
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float src1 = nz(source[1])
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filt2 := filt1
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filt1 := filt
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filt := c1 * (price + src1) * 0.5 + c2 * filt1 + c3 * filt2
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// --- Circular buffer to store filtered values for lookback ---
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var array<float> buf = array.new_float(period + 1, 0.0)
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var int head = 0
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array.set(buf, head, filt)
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int count = math.min(bar_index + 1, period)
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// --- Slope: (Filt[Length] - Filt) / Length ---
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int lag_idx = (head - period + period + 1) % (period + 1)
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float filt_lag = array.get(buf, lag_idx)
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float slope = (filt_lag - filt) / period
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// --- Sum the differences ---
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// Sum = Σ(i=1..Length) [(Filt + i*Slope) - Filt[i]] / Length
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float the_sum = 0.0
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if count >= period
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for i = 1 to period
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int idx = (head - i + period + 1) % (period + 1)
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float filt_i = array.get(buf, idx)
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the_sum += (filt + float(i) * slope) - filt_i
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the_sum /= period
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// --- Advance head ---
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head := (head + 1) % (period + 1)
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// --- Normalize in terms of Standard Deviations ---
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// MS = 0.04 * Sum² + 0.96 * MS[1] (exponential RMS)
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var float ms = 0.0
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ms := 0.04 * the_sum * the_sum + 0.96 * ms
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float result = 0.0
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if ms > 0.0
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result := the_sum / math.sqrt(ms)
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result
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// ── Inputs ──
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int p_period = input.int(20, "Period", minval = 2)
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float p_src = input.source(close, "Source")
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// ── Calculation ──
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float out = reflex(p_src, p_period)
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// ── Plot ──
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plot(out, "REFLEX", color.yellow, 2)
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hline(0, "Zero", color.gray)
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hline(1.0, "+1σ", color.new(color.red, 60))
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hline(-1.0, "-1σ", color.new(color.green, 60))
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