// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Correlation Trend Indicator (CTI)", "CTI", overlay=false)

//@function Calculates Pearson correlation between price and linear time index
//@param source Series to calculate correlation from
//@param period Lookback period for correlation window
//@returns CTI value (-1 to +1) measuring linear trend strength
//@optimized O(1) complexity using incremental running sums
cti(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 sumY2 = 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
            sumY2 -= oldest * oldest
            sumXY -= sumY
            sumXY += (period - 1) * source
        else
            sumXY += count * source
            count += 1

        sumY += source
        sumY2 += source * source
        array.set(buffer, head, source)
        head := (head + 1) % period

        if count < 2
            na
        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
            float denomY = n * sumY2 - sumY * sumY

            float denom = denomX * denomY
            if denom <= 0.0
                0.0
            else
                float numer = n * sumXY - sumX * sumY
                float r = numer / math.sqrt(denom)
                math.max(-1.0, math.min(1.0, r))

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

// Inputs
i_source = input.source(close, "Source")
i_period = input.int(20, "Period", minval=2, maxval=5000)

// Calculation
cti_value = cti(i_source, i_period)

// Plot
plot(cti_value, "CTI", color.new(color.yellow, 0), 2)
hline(0, "Zero", color=color.gray, linestyle=hline.style_dotted)
hline(0.5, "Upper", color=color.gray, linestyle=hline.style_dotted)
hline(-0.5, "Lower", color=color.gray, linestyle=hline.style_dotted)