// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Forecast Oscillator (FOSC)", "FOSC", overlay=false)

//@function Calculates Forecast Oscillator — percentage deviation from linear regression forecast
//@param source Series to calculate from
//@param period Lookback period for linear regression
//@returns FOSC value: 100 * (source - LinReg) / source
//@optimized O(1) complexity using incremental running sums for linear regression
fosc(series float source, simple int period) =>
    if period <= 0
        runtime.error("Period must be greater than 0")
    if period > 5000
        runtime.error("Period exceeds maximum of 5000")

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

    if na(source)
        na
    else
        float oldest = array.get(buffer, head)
        if not na(oldest)
            sumY -= oldest
            sumXY -= sumY
            sumXY += (period - 1) * source
        else
            sumXY += count * source
            count += 1

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

        if count < 2
            0.0
        else
            float n = float(count)
            float sumX = n * (n - 1.0) / 2.0
            float sumX2 = n * (n - 1.0) * (2.0 * n - 1.0) / 6.0
            float denomX = n * sumX2 - sumX * sumX

            if denomX == 0.0
                0.0
            else
                float slope = (n * sumXY - sumX * sumY) / denomX
                float intercept = (sumY - slope * sumX) / n
                float forecast = slope * (n - 1.0) + intercept

                source != 0.0 ? (source - forecast) / source * 100.0 : 0.0

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

// Inputs
i_source = input.source(close, "Source")
i_period = input.int(14, "Period", minval=2, maxval=5000)

// Calculation
float result = fosc(i_source, i_period)

// Plot
plot(result, "FOSC", color=color.yellow, linewidth=2)
hline(0, "Zero", color=color.gray, linestyle=hline.style_dotted)