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Miha Kralj
35a6702b06
Deep review of all indicator categories verified .md headers against .cs WarmupPeriod, parameters, inputs, and outputs. Fixes include warmup corrections, parameter documentation, output type accuracy, and Pine Script alignment.
70 lines
3.2 KiB
Plaintext
70 lines
3.2 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("NMA - Natural Moving Average", "NMA", overlay=true)
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// ── Functions ──────────────────────────────────────────────────────────
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// @function Calculates the Natural Moving Average (Jim Sloman, Ocean Theory pgs 63-70).
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// Adaptive IIR filter where the smoothing ratio derives from volatility-weighted
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// sqrt-kernel analysis of log-price movements over a lookback window.
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// Step 1: ln = log(src) × 1000 (scaled natural log)
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// Step 2: For i=0..period-1, accumulate:
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// oi = |ln[i] - ln[i+1]| (bar-to-bar log-price volatility)
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// num += oi × (√(i+1) - √i) (sqrt-differenced weight emphasizes recent bars)
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// denom += oi (total volatility normalization)
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// Step 3: ratio = num / denom (adaptive smoothing factor ∈ [0,1])
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// Step 4: nma = nma[1] + ratio × (src - nma[1]) (IIR adaptive EMA step)
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// When volatility concentrates in recent bars → ratio ≈ 1 → fast tracking.
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// When volatility is spread uniformly → ratio ≈ 1/√period → heavy smoothing.
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// @param source Series to smooth
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// @param period Lookback window for volatility analysis (must be > 0)
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// @returns NMA value
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nma(series float source, simple int period) =>
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float src = nz(source)
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// Step 1: scaled natural log of price
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// Use circular buffer to store log-scaled values for lookback
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var array<float> lnBuf = array.new_float(period + 1, 0.0)
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var int head = 0
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float lnVal = src > 0 ? math.log(src) * 1000.0 : 0.0
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array.set(lnBuf, head, lnVal)
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// Step 2: compute volatility-weighted sqrt ratio over lookback
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float num = 0.0
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float denom = 0.0
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int bars = math.min(bar_index + 1, period)
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for i = 0 to bars - 1
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int idx0 = (head - i + period + 1) % (period + 1)
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int idx1 = (head - i - 1 + period + 1) % (period + 1)
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float oi = math.abs(array.get(lnBuf, idx0) - array.get(lnBuf, idx1))
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num += oi * (math.sqrt(i + 1) - math.sqrt(i))
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denom += oi
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// Advance head for next bar
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head := (head + 1) % (period + 1)
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// Step 3: adaptive ratio
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float ratio = denom != 0.0 ? num / denom : 0.0
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// Step 4: IIR adaptive EMA step
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var float result = 0.0
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if bar_index == 0
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result := src
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else
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result := result + ratio * (src - result)
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result
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// ── Inputs ─────────────────────────────────────────────────────────────
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int i_period = input.int(40, "Period", minval=1)
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float i_source = input.source(close, "Source")
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// ── Calculation ────────────────────────────────────────────────────────
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float value = nma(i_source, i_period)
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// ── Plot ───────────────────────────────────────────────────────────────
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plot(value, "NMA", color.yellow, 2)
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