// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Weighted Average (WAVG)", "WAVG", overlay=true)

//@function Calculates rolling linearly-weighted average over a lookback window
//@param source Series to evaluate (typically close)
//@param period Lookback period (number of bars)
//@returns Weighted average where weight[i] = position from oldest (1) to newest (period)
//@description WAVG assigns linearly increasing weights to the lookback window:
//    weight_i = i + 1   for i = 0 (oldest) to period-1 (newest)
//    WAVG = Σ(weight_i × value_i) / Σ(weight_i)
//    Σ(weight_i) = period × (period + 1) / 2
//  Uses a circular buffer for O(1) updates per bar. On each new bar:
//    1. Subtract the departing oldest value's contribution from weightedSum
//    2. Shift all existing weights down by 1 (subtract runningSum from weightedSum)
//    3. Add the new value with weight = count (current fill level)
//  runningSum tracks the unweighted sum for the shift operation.
//  §3 count-based warmup: during filling, actual count < period, and
//  denominator = count × (count + 1) / 2.
//  This is mathematically identical to WMA but categorized as a statistical measure.
wavg(series float source, simple int period) =>
    if period <= 0
        runtime.error("Period must be greater than 0")

    var array<float> buffer = array.new_float(period, na)
    var int head            = 0
    var float weightedSum   = 0.0
    var float runningSum    = 0.0
    var int count           = 0

    float srcVal = nz(source)
    float oldest = array.get(buffer, head)

    if not na(oldest)
        runningSum -= oldest
    else
        count += 1

    weightedSum -= runningSum
    runningSum  += srcVal
    weightedSum += float(count) * srcVal

    array.set(buffer, head, srcVal)
    head := (head + 1) % period

    float denom = float(count) * float(count + 1) / 2.0
    denom > 0.0 ? weightedSum / denom : srcVal

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

// Inputs
i_source = input.source(close, "Source")
i_period = input.int(14, "Period", minval=1)

// Calculation
wavg_value = wavg(i_source, i_period)

// Plot
plot(wavg_value, "WAVG", color=color.yellow, linewidth=2)