Hurst Exponent (HURST)

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Hurst Exponent (HURST)", "HURST", overlay=false, precision=4)

//@function Calculates the Hurst Exponent for a given series and lookback period.
//@param source series float The input series.
//@param length int The lookback period for Hurst Exponent calculation.
//@returns series float The Hurst Exponent value.
hurst(series float source, simple int length) =>
    if length <= 10 
        runtime.error("Length must be greater than 10 for Hurst Exponent.")
        na
    log_returns = math.log(source / source[1])
    min_n = 10
    max_n = length / 2
    if max_n < min_n
        runtime.error("Length too short for sub-period division.")
        na
    array<float> log_n_values = array.new_float(0)
    array<float> log_rs_values = array.new_float(0)
    for n = min_n to max_n
        if n == 0
            continue
        num_sub_periods = math.floor(length / n)
        if num_sub_periods == 0
            continue
        rs_sum = 0.0
        for i = 0 to num_sub_periods - 1
            start_index = i * n
            float[] sub_period_returns = array.new_float(n)
            for j = 0 to n - 1
                array.set(sub_period_returns, j, log_returns[start_index + j])
            sub_period_sum = 0.0
            for k_val = 0 to n - 1
                sub_period_sum += array.get(sub_period_returns, k_val)
            sub_mean = sub_period_sum / n
            float[] cum_dev = array.new_float(n)
            current_sum = 0.0
            for j = 0 to n - 1
                current_sum += (array.get(sub_period_returns, j) - sub_mean)
                array.set(cum_dev, j, current_sum)
            range_val = array.max(cum_dev) - array.min(cum_dev)
            variance_sum = 0.0
            for j = 0 to n - 1
                variance_sum += math.pow(array.get(sub_period_returns, j) - sub_mean, 2)
            std_dev_val_corrected = math.sqrt(variance_sum / n)
            if std_dev_val_corrected > 0
                rs_sum += range_val / std_dev_val_corrected
        if num_sub_periods > 0
            avg_rs = rs_sum / num_sub_periods
            if avg_rs > 0 
                array.push(log_n_values, math.log(n))
                array.push(log_rs_values, math.log(avg_rs))
    if array.size(log_n_values) < 2 
        na
    else
        m = array.size(log_n_values)
        sum_x = 0.0
        sum_y = 0.0
        sum_xy = 0.0
        sum_x_sq = 0.0
        for i = 0 to m - 1
            xi = array.get(log_n_values, i)
            yi = array.get(log_rs_values, i)
            sum_x += xi
            sum_y += yi
            sum_xy += xi * yi
            sum_x_sq += xi * xi
        denominator = m * sum_x_sq - math.pow(sum_x, 2)
        if denominator == 0
            na 
        else
            (m * sum_xy - sum_x * sum_y) / denominator

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

// Inputs
i_source = input.source(close, "Source")
i_length = input.int(100, "Length", minval=20, tooltip="Lookback period for Hurst Exponent calculation. Min 20.")

// Calculation
hurstValue = hurst(i_source, i_length)

// Plot
plot(hurstValue, "Hurst Exponent", color=color.yellow, linewidth=2)