Dynamic Momentum Index (DYMI)

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Dynamic Momentum Index (DYMI)", "DYMI", overlay=false)

//@description Dynamic Momentum Index by Tushar Chande and Stanley Kroll (1994).
// A three-stage pipeline that produces a volatility-adaptive RSI:
// Stage 1: Dual circular-buffer StdDev → volatility ratio V = σ_short / σ_long
// Stage 2: dynamic_period = clamp(round(basePeriod / V), minPeriod, maxPeriod)
// Stage 3: Wilder RMA RSI with adaptive alpha = 1 / dynamic_period
// When price volatility is high V > 1, the period shortens → faster response.
// When volatility is low V < 1, the period lengthens → smoother output.

//@function Calculates StdDev over a circular buffer of given period
//@param source Price series
//@param period Window size
//@returns Population standard deviation of the window
stddev_circ(series float source, simple int period) =>
    var array<float> buf = array.new_float(period, na)
    var int head = 0
    var int count = 0
    var float sumV = 0.0
    var float sumSq = 0.0

    float oldest = array.get(buf, head)
    if not na(oldest)
        sumV  -= oldest
        sumSq -= oldest * oldest

    float val = na(source) ? 0.0 : source
    array.set(buf, head, val)
    sumV  += val
    sumSq += val * val
    head := (head + 1) % period
    if count < period
        count += 1

    float mean = sumV / count
    float variance = sumSq / count - mean * mean
    float sd = variance > 0.0 ? math.sqrt(variance) : 0.0
    sd

//@function Calculates Wilder's RMA RSI with warmup compensation and adaptive alpha
//@param source Close price series
//@param dynPeriod Dynamic period (integer, already clamped)
//@returns RSI value in [0, 100]
rsi_wilder(series float source, series int dynPeriod) =>
    var float prevVal  = na
    var float avgGain  = 0.0
    var float avgLoss  = 0.0
    var float e        = 1.0
    var bool  warmup   = true

    float result = 50.0

    if not na(source)
        if na(prevVal)
            prevVal := source
        else
            float alpha  = 1.0 / dynPeriod
            float beta   = 1.0 - alpha
            float change = source - prevVal
            float gain   = change > 0.0 ? change : 0.0
            float loss   = change < 0.0 ? -change : 0.0
            prevVal := source

            avgGain := alpha * gain + beta * avgGain
            avgLoss := alpha * loss + beta * avgLoss

            if warmup
                e *= beta
                float c    = e > 1e-10 ? 1.0 / (1.0 - e) : 1.0
                float aG   = avgGain * c
                float aL   = avgLoss * c
                float total = aG + aL
                result := total != 0.0 ? 100.0 * aG / total : 50.0
                if e <= 1e-10
                    warmup := false
            else
                float total = avgGain + avgLoss
                result := total != 0.0 ? 100.0 * avgGain / total : 50.0

    result

//@function Calculates Dynamic Momentum Index
//@param source Close price series
//@param basePeriod Base RSI period (default 14)
//@param shortPeriod Short StdDev window (default 5)
//@param longPeriod Long StdDev window (default 10)
//@param minPeriod Minimum dynamic period (default 3)
//@param maxPeriod Maximum dynamic period (default 30)
//@returns DYMI value in [0, 100]
//@optimized Uses circular buffers for O(1) StdDev; adaptive Wilder RMA for RSI
dymi(series float source, simple int basePeriod, simple int shortPeriod, simple int longPeriod, simple int minPeriod, simple int maxPeriod) =>
    if basePeriod < 2 or shortPeriod < 2 or longPeriod <= shortPeriod or minPeriod < 2 or maxPeriod < minPeriod
        runtime.error("Invalid DYMI parameters")

    // Stage 1: dual StdDev volatility ratio
    float sdShort = stddev_circ(source, shortPeriod)
    float sdLong  = stddev_circ(source, longPeriod)

    float v = sdLong > 1e-10 ? sdShort / sdLong : 1.0

    // Stage 2: dynamic period
    int rawPeriod  = v > 1e-10 ? math.round(basePeriod / v) : maxPeriod
    int dynPeriod  = math.max(minPeriod, math.min(maxPeriod, rawPeriod))

    // Stage 3: adaptive Wilder RSI
    float result = rsi_wilder(source, dynPeriod)
    math.max(0.0, math.min(100.0, result))

// ---------- Main loop ----------

i_basePeriod  = input.int(14, "Base RSI Period",   minval=2,  maxval=500)
i_shortPeriod = input.int(5,  "Short StdDev Period", minval=2,  maxval=500)
i_longPeriod  = input.int(10, "Long StdDev Period",  minval=2,  maxval=500)
i_minPeriod   = input.int(3,  "Min Period",          minval=2,  maxval=500)
i_maxPeriod   = input.int(30, "Max Period",          minval=2,  maxval=500)
i_source      = input.source(close, "Source")

dymi_val = dymi(i_source, i_basePeriod, i_shortPeriod, i_longPeriod, i_minPeriod, i_maxPeriod)

plot(dymi_val, "DYMI", color=color.yellow, linewidth=2)
hline(70, "Overbought", color=color.gray, linestyle=hline.style_dotted)
hline(50, "Midline",    color=color.gray, linestyle=hline.style_dotted)
hline(30, "Oversold",   color=color.gray, linestyle=hline.style_dotted)