Standard Error of Regression (STDERR)

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Standard Error of Regression (STDERR)", "STDERR", overlay=false, precision=8)

//@function Calculates the standard error of the linear regression estimate over the specified period.
//@param src {series float} Source series.
//@param len {simple int} Lookback length. `len` >= 3.
//@returns {series float} Standard error of regression for `len` bars back. Returns `na` if not enough data.
stderr(series float src, simple int len) =>
    if len < 3
        runtime.error("Period must be at least 3")
    var int p = math.max(3, len)
    var array<float> buffer = array.new_float(p, na)
    var int head = 0, var int count = 0

    // Update circular buffer
    float oldest = array.get(buffer, head)
    if not na(oldest)
        count -= 1
    float val = nz(src)
    array.set(buffer, head, val)
    count += 1
    head := (head + 1) % p

    if count < 3
        na
    else
        // Calculate regression coefficients
        int n = count
        int start = count < p ? 0 : head
        float sumX = 0.0, float sumY = 0.0
        float sumXY = 0.0, float sumX2 = 0.0
        for i = 0 to n - 1
            int idx = (start + i) % p
            float y_val = array.get(buffer, idx)
            float x_val = float(i)
            sumX += x_val
            sumY += y_val
            sumXY += x_val * y_val
            sumX2 += x_val * x_val

        float nf = float(n)
        float denom = nf * sumX2 - sumX * sumX
        if denom == 0
            0.0
        else
            float slope = (nf * sumXY - sumX * sumY) / denom
            float intercept = (sumY - slope * sumX) / nf

            // Calculate sum of squared residuals
            float ssr = 0.0
            for i = 0 to n - 1
                int idx = (start + i) % p
                float y_val = array.get(buffer, idx)
                float predicted = intercept + slope * float(i)
                float residual = y_val - predicted
                ssr += residual * residual

            math.sqrt(ssr / (nf - 2.0))


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

// Inputs
i_period = input.int(14, "Period", minval=3)
i_source = input.source(close, "Source")

// Calculation
stderr_value = stderr(i_source, i_period)

// Plot
plot(stderr_value, "Stderr", color=color.yellow, linewidth=2)