mirror of
https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
94 lines
2.9 KiB
Plaintext
94 lines
2.9 KiB
Plaintext
// Licensed under the Apache License, Version 2.0
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// © mihakralj
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// Indicator algorithm (C) 2017 John F. Ehlers
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//@version=6
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indicator("Ehlers Reverse EMA (REVERSEEMA)", "REVERSEEMA", overlay=false)
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//@function Calculates Ehlers Reverse EMA using Z-transform inversion of EMA smoothing
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//@param source Series to calculate Reverse EMA from
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//@param period Lookback period for the base EMA (>= 1)
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//@returns Reverse EMA value with lag removed via 8-stage cascaded inversion
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//@optimized Uses warmup-compensated EMA with O(1) cascaded reverse stages per bar
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reverseema(series float source, simple int period) =>
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if period <= 0
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runtime.error("Period must be positive")
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float src = na(source) ? 0.0 : source
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// EMA smoothing factor from period: alpha = 2/(period+1)
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float a = 2.0 / (period + 1)
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float cc = 1.0 - a
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float beta = cc
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// Precompute powers of cc for the 8 reverse stages
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// Stage k uses cc^(2^(k-1)): 1, 2, 4, 8, 16, 32, 64, 128
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float cc2 = cc * cc
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float cc4 = cc2 * cc2
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float cc8 = cc4 * cc4
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float cc16 = cc8 * cc8
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float cc32 = cc16 * cc16
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float cc64 = cc32 * cc32
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float cc128 = cc64 * cc64
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// --- Forward EMA with warmup compensator ---
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var bool warmup = true
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var float e = 1.0
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var float ema_raw = 0.0
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var float ema_val = 0.0
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ema_raw := a * (src - ema_raw) + ema_raw
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if warmup
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e *= beta
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float comp = 1.0 / (1.0 - e)
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ema_val := comp * ema_raw
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warmup := e > 1e-10
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else
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ema_val := ema_raw
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// --- 8-stage cascaded reverse EMA ---
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// Each stage: RE_k[n] = cc^(2^(k-1)) * RE_{k-1}[n] + RE_{k-1}[n-1]
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// RE1 uses EMA as input: RE1[n] = cc * EMA[n] + EMA[n-1]
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var float re1 = 0.0
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var float re2 = 0.0
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var float re3 = 0.0
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var float re4 = 0.0
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var float re5 = 0.0
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var float re6 = 0.0
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var float re7 = 0.0
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var float re8 = 0.0
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float prev_ema = nz(ema_val[1])
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float prev_re1 = nz(re1[1])
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float prev_re2 = nz(re2[1])
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float prev_re3 = nz(re3[1])
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float prev_re4 = nz(re4[1])
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float prev_re5 = nz(re5[1])
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float prev_re6 = nz(re6[1])
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float prev_re7 = nz(re7[1])
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re1 := cc * ema_val + prev_ema
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re2 := cc2 * re1 + prev_re1
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re3 := cc4 * re2 + prev_re2
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re4 := cc8 * re3 + prev_re3
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re5 := cc16 * re4 + prev_re4
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re6 := cc32 * re5 + prev_re5
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re7 := cc64 * re6 + prev_re6
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re8 := cc128 * re7 + prev_re7
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// Signal = EMA - alpha * RE8
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float signal = ema_val - a * re8
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na(source) ? na : signal
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// ---------- Main loop ----------
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// Inputs
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i_period = input.int(20, "Period", minval=1, tooltip="Lookback period for the base EMA")
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i_source = input.source(close, "Source")
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// Calculation
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reverseema_value = reverseema(i_source, i_period)
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// Plot
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plot(reverseema_value, "REVERSEEMA", color=color.yellow, linewidth=2)
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hline(0, "Zero", color=color.gray)
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