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

//@function Calculates Ahrens Moving Average using midpoint correction between current and lagged MA values
//@param source Series to smooth
//@param period Lookback length for the lag component and smoothing divisor
//@returns Ahrens MA value — a recursive IIR filter that adjusts toward source minus the midpoint of its current and lagged states
//@algorithm ahma = ahma[1] + (source - (ahma[1] + ahma[period]) / 2) / period
//@reference Richard D. Ahrens, "Build A Better Moving Average" (Stocks & Commodities V.31:11, October 2013)
//@optimized O(1) per bar via circular buffer for lagged MA state; O(period) memory for the ring buffer
ahrens(series float source, simple int period) =>

    // Circular buffer to store past ahma values for period-bar lookback
    var array<float> buffer = array.new_float(period, na)
    var int head = 0
    var float result = na

    if not na(source)
        float prev = nz(result, source)
        float lagged = nz(array.get(buffer, head), source)

        // Ahrens formula: ahma = prev + (source - midpoint(prev, lagged)) / period
        float midpoint = (prev + lagged) * 0.5
        result := prev + (source - midpoint) / float(period)

        // Store current result in circular buffer and advance head
        array.set(buffer, head, result)
        head := (head + 1) % period
    result

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

// Inputs
i_period = input.int(9, "Period", minval=1)
i_source = input.source(close, "Source")

// Calculation
ahrens_value = ahrens(i_source, i_period)

// Plot
plot(ahrens_value, "AHRENS", color=color.yellow, linewidth=2)