// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Holt-Winters Moving Average (HWMA)", "HWMA", overlay=true)

//@function Calculates HWMA using triple exponential smoothing with level, velocity, and acceleration components
//@param source Series to calculate HWMA from
//@param alpha Level smoothing factor
//@param beta Velocity smoothing factor
//@param gamma Acceleration smoothing factor
//@param period When used, calculate alpha/beta/gamma from period
//@returns HWMA value from first bar with proper compensation
//@optimized Uses triple exponential smoothing with O(1) complexity per bar
hwma(series float source, float alpha=0.0, float beta=0.0, float gamma=0.0, simple int period=0) =>
    float a = period > 0 ? 2.0 / (float(period) + 1.0) : alpha
    float b = period > 0 ? 1.0 / float(period) : beta
    float g = period > 0 ? 1.0 / float(period) : gamma
    var float F = na
    var float V = 0.0
    var float A = 0.0
    if na(source)
        if na(F)
            na
        else
            float prevF = F
            float prevV = V
            float prevA = A
            F := prevF + prevV + 0.5 * prevA
            V := prevV + prevA
            A := 0.9 * prevA
            F
    else
        if na(F)
            F := source
            F
        else
            float prevF = F
            float prevV = V
            float prevA = A
            F := a * source + (1.0 - a) * (prevF + prevV + 0.5 * prevA)
            V := b * (F - prevF) + (1.0 - b) * (prevV + prevA)
            A := g * (V - prevV) + (1.0 - g) * prevA
            F + V + 0.5 * A

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

// Inputs
i_period = input.int(10, "Period", minval=1)
i_source = input.source(close, "Source")

// Calculation
hwma_value = hwma(i_source, period=i_period)

// Plot
plot(hwma_value, "HWMA", color=color.yellow, linewidth=2)