Ehlers Deviation-Scaled Oscillator (DSO)

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Ehlers Deviation-Scaled Oscillator (DSO)", "DSO", overlay = false)

//@function Ehlers Deviation-Scaled Oscillator — a Fisher-transformed, RMS-normalized
//          Super Smoother oscillator. Applies a 2-pole Super Smoother filter to the
//          whitened input (Close - Close[2]), computes a rolling RMS over the period,
//          normalizes the filtered signal by RMS, then applies the Fisher Transform
//          with ±0.99 clamping. Output is an unbounded oscillator (typically ±3).
//@param source Series to analyze
//@param period Lookback window / assumed cycle period (>= 2)
//@returns DSO oscillator value (Fisher-transformed, unbounded)
//@reference Ehlers, J.F. (2018). "A Fisherized Deviation-Scaled Oscillator."
//           Technical Analysis of Stocks & Commodities, Oct 2018.
//@optimized O(1) per bar via running sum circular buffer for RMS
dso(series float source, simple int period) =>
    if period < 2
        runtime.error("Period must be at least 2")

    float price = nz(source)

    // --- Super Smoother coefficients (2-pole Butterworth at half-period cutoff) ---
    float half_period = period * 0.5
    float a1 = math.exp(-1.414 * math.pi / half_period)
    float b1 = 2.0 * a1 * math.cos(1.414 * 180.0 / half_period)
    float c2 = b1
    float c3 = -(a1 * a1)
    float c1 = 1.0 - c2 - c3

    // --- Whitening: zeros at DC and Nyquist ---
    float zeros = price - nz(source[2])

    // --- 2-pole Super Smoother filter ---
    var float filt  = 0.0
    var float filt1 = 0.0
    var float filt2 = 0.0
    float zeros1 = nz(zeros[1])
    filt2 := filt1
    filt1 := filt
    filt := c1 * 0.5 * (zeros + zeros1) + c2 * filt1 + c3 * filt2

    // --- Rolling RMS via circular buffer ---
    var array<float> buf = array.new_float(period, 0.0)
    var int head = 0
    var float sum_sq = 0.0

    float filt_sq = filt * filt
    float old_sq = array.get(buf, head)
    array.set(buf, head, filt_sq)
    sum_sq := sum_sq - old_sq + filt_sq
    head := (head + 1) % period

    float rms = math.sqrt(math.max(sum_sq / period, 1e-10))

    // --- Scale by RMS ---
    float scaled_filt = rms != 0.0 ? filt / rms : 0.0

    // --- Fisher Transform (clamp to ±0.99) ---
    float clamped = math.max(-0.99, math.min(0.99, scaled_filt))
    float fisher_filt = 0.5 * math.log((1.0 + clamped) / (1.0 - clamped))

    fisher_filt

// ── Inputs ──
int   p_period = input.int(40, "Period", minval = 2)
float p_src    = input.source(close, "Source")

// ── Calculation ──
float out = dso(p_src, p_period)

// ── Plot ──
plot(out, "DSO", color.yellow, 2)
hline(0, "Zero", color.gray)
hline(2.0, "+2", color.new(color.red, 60))
hline(-2.0, "-2", color.new(color.green, 60))