R² Coefficient of Determination (RSQUARED)

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("R² Coefficient of Determination (RSQUARED)", "RSQUARED")

//@function Calculates the R-squared (Coefficient of Determination) between two sources
//@param source1 First series to compare (actual)
//@param source2 Second series to compare (predicted)
//@param period Lookback period for averaging
//@returns R-squared value averaging over the specified period
rsquared(series float source1, series float source2, simple int period) =>
    if period <= 0
        runtime.error("Period must be greater than 0")
    int p = math.min(math.max(1, period), 4000)
    var float sum_source1 = 0.0
    var float[] buffer_source1 = array.new_float(p, na)
    var int head_source1 = 0
    var int valid_count_source1 = 0
    float oldest_source1 = array.get(buffer_source1, head_source1)
    if not na(oldest_source1)
        sum_source1 := sum_source1 - oldest_source1
        valid_count_source1 := valid_count_source1 - 1
    if not na(source1)
        sum_source1 := sum_source1 + source1
        valid_count_source1 := valid_count_source1 + 1
    array.set(buffer_source1, head_source1, source1)
    head_source1 := (head_source1 + 1) % p
    float mean_source1 = valid_count_source1 > 0 ? sum_source1 / valid_count_source1 : source1
    float squared_residual = math.pow(source1 - source2, 2)
    float total_ss = math.pow(source1 - mean_source1, 2)
    var float sum_squared_residual = 0.0
    var float[] buffer_squared_residual = array.new_float(p, na)
    var int head_squared_residual = 0
    var int valid_count_squared_residual = 0
    float oldest_squared_residual = array.get(buffer_squared_residual, head_squared_residual)
    if not na(oldest_squared_residual)
        sum_squared_residual := sum_squared_residual - oldest_squared_residual
        valid_count_squared_residual := valid_count_squared_residual - 1
    if not na(squared_residual)
        sum_squared_residual := sum_squared_residual + squared_residual
        valid_count_squared_residual := valid_count_squared_residual + 1
    array.set(buffer_squared_residual, head_squared_residual, squared_residual)
    head_squared_residual := (head_squared_residual + 1) % p
    var float sum_total_ss = 0.0
    var float[] buffer_total_ss = array.new_float(p, na)
    var int head_total_ss = 0
    var int valid_count_total_ss = 0
    float oldest_total_ss = array.get(buffer_total_ss, head_total_ss)
    if not na(oldest_total_ss)
        sum_total_ss := sum_total_ss - oldest_total_ss
        valid_count_total_ss := valid_count_total_ss - 1
    if not na(total_ss)
        sum_total_ss := sum_total_ss + total_ss
        valid_count_total_ss := valid_count_total_ss + 1
    array.set(buffer_total_ss, head_total_ss, total_ss)
    head_total_ss := (head_total_ss + 1) % p
    float rss = valid_count_squared_residual > 0 ? sum_squared_residual : squared_residual
    float tss = valid_count_total_ss > 0 ? sum_total_ss : total_ss
    tss != 0 ? 1 - (rss / tss) : 1.0


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

// Inputs
i_source1 = input.source(close, "Source")
i_period = input.int(100, "Period", minval=1)
i_source2 = ta.ema(i_source1, i_period)

// Calculation
score = rsquared(i_source1, i_source2, i_period)

// Plot
plot(score, "R²", color.new(color.red, 60, color=color.yellow, linewidth=2), linewidth = 2, style = plot.style_area)
plot(i_source2, "EMA", color.new(color.yellow, 0, linewidth=2), linewidth = 1, style = plot.style_line, force_overlay = true)