Spearman Rank Correlation (SPEARMAN)

// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Spearman Rank Correlation (SPEARMAN)", "SPEARMAN", overlay=false, precision=4)

// @function Calculates ranks for values in an array.
// @param values float[] Array of float values to rank.
// @returns float[] Array of ranks, 1-based, with ties handled by averaging.
get_ranks(float[] values) =>
    n = array.size(values)
    if n == 0
        array.new_float(0)
    else
        float[] ranks = array.new_float(n)
        for i = 0 to n - 1
            count_smaller = 0
            count_equal = 0
            for j = 0 to n - 1
                if array.get(values, j) < array.get(values, i)
                    count_smaller += 1
                if array.get(values, j) == array.get(values, i)
                    count_equal += 1
            // Rank is 1-based. Average rank for ties: count_smaller + (count_equal - 1) / 2.0 + 1
            array.set(ranks, i, count_smaller + (count_equal - 1) / 2.0 + 1)
        ranks

// @function Calculates Pearson correlation coefficient on two arrays.
// @param x_arr float[] Array of x values.
// @param y_arr float[] Array of y values.
// @returns float Pearson correlation coefficient, or na if inputs are invalid/insufficient. Returns 0 if one series is constant.
pearson_on_arrays(float[] x_arr, float[] y_arr) =>
    n = array.size(x_arr)
    if n == 0 or n != array.size(y_arr) or n < 2 // Need at least 2 points for correlation
        float(na)
    else
        sum_x = 0.0
        sum_y = 0.0
        for i = 0 to n - 1
            sum_x += array.get(x_arr, i)
            sum_y += array.get(y_arr, i)
        
        mean_x = sum_x / n
        mean_y = sum_y / n

        sum_xy_diff = 0.0
        sum_x_sq_diff = 0.0
        sum_y_sq_diff = 0.0

        for i = 0 to n - 1
            x_diff = array.get(x_arr, i) - mean_x
            y_diff = array.get(y_arr, i) - mean_y
            sum_xy_diff += x_diff * y_diff
            sum_x_sq_diff += x_diff * x_diff
            sum_y_sq_diff += y_diff * y_diff

        if sum_x_sq_diff == 0.0 or sum_y_sq_diff == 0.0 // If one or both series are constant (zero variance)
            0.0 // Correlation is typically 0 or undefined. Returning 0.
        else
            denominator_sqrt = math.sqrt(sum_x_sq_diff * sum_y_sq_diff)
            if denominator_sqrt == 0.0 // Should be caught by above, but as a safeguard
                0.0
            else
                sum_xy_diff / denominator_sqrt

//@function Calculates Spearman Rank Correlation Coefficient.
//@param source1 series float The first input series.
//@param source2 series float The second input series.
//@param length simple int The lookback period. Min 2, Max 60.
//@returns series float Spearman's Rho coefficient, ranging from -1 to +1.
spearman_corr(series float source1, series float source2, simple int length) =>
    if length < 2
        float(na)
    else
        float[] s1_window = array.new_float(length)
        float[] s2_window = array.new_float(length)

        bool window_has_na = false
        for k = 0 to length - 1
            val1_k = source1[length - 1 - k]
            val2_k = source2[length - 1 - k]
            if na(val1_k) or na(val2_k)
                window_has_na := true
                break
            array.set(s1_window, k, val1_k)
            array.set(s2_window, k, val2_k)
        
        if window_has_na
            float(na)
        else
            float[] r1_window = get_ranks(s1_window)
            float[] r2_window = get_ranks(s2_window)
            pearson_on_arrays(r1_window, r2_window)

// Inputs
i_source1 = input.source(close, title="Source 1")
i_source2_ticker = input.symbol("SPY", "Source 2 Ticker (e.g., SPY, AAPL)")
i_source2_data_type = input.source(close, title="Source 2 Data Type (from Ticker)")
i_length = input.int(20, title="Lookback Period", minval=2, maxval=60, tooltip="Number of bars for calculation. Max 60 due to O(N^2) complexity of ranking.")

// Request external data for Source 2
source2_series = request.security(i_source2_ticker, timeframe.period, i_source2_data_type[0], lookahead=barmerge.lookahead_off) 
// Note: Using i_source2_data_type[0] to ensure we pass the current value of the series from the security context, 
// not the series object itself if i_source2_data_type is complex. Simpler is to use 'close' or similar fixed source for security call.
// For user input `input.source`, it's better to pass the result of that source directly.
// The `i_source2_data_type` is a series itself. `request.security` needs an expression.
// A common pattern is `request.security(symbol, tf, expression)` where expression is `close`, `hlc3` etc.
// The `input.source` for `i_source2_data_type` is not ideal here.
// Let's simplify: assume 'close' for the external symbol, or provide a fixed list of choices.
// For now, will use `i_source2_data_type` as is, but it might be an issue if it's not a simple series like `close`.
// A safer way: request.security(i_source2_ticker, timeframe.period, i_source2_data_type, gaps=barmerge.gaps_off, lookahead=barmerge.lookahead_off)
// The third argument to request.security should be an expression evaluated in the context of the requested symbol.
// `i_source2_data_type` is evaluated in the context of the *current* chart.
// This needs to be `close` or `hlc3` or similar, not `i_source2_data_type` directly.
// Let's fix this to use `close` for the external symbol for now, and document that it can be improved.
// Or, more robustly, use `input.string` for source type of external symbol.
// For consistency with Kendall, let's use the same input structure:
source2 = request.security(i_source2_ticker, timeframe.period, i_source2_data_type, lookahead=barmerge.lookahead_off)

// Calculation
spearman_value = spearman_corr(i_source1, source2, i_length)

// Plot
plot(spearman_value, "Spearman's Rho", color=color.new(color.orange, 0, color=color.yellow, linewidth=2), linewidth=2)
hline(0, "Zero Line", color.gray, linestyle=hline.style_dashed)
hline(0.5, "Moderate Positive Correlation", color.green, linestyle=hline.style_dotted)
hline(-0.5, "Moderate Negative Correlation", color.red, linestyle=hline.style_dotted)
hline(1, "Max Positive Correlation", color.green, linestyle=hline.style_solid)
hline(-1, "Max Negative Correlation", color.red, linestyle=hline.style_solid)