// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Theil's U Statistic", "TheilU", overlay=false)

//@function Calculates Theil's U Statistic (U1)
//@param   actual Series of actual values
//@param   predicted Series of predicted/forecast values
//@param   length Rolling window for calculation
//@returns Theil's U value (0 to 1+ range)
theil_u(series float actual, series float predicted, simple int length) =>
    float epsilon = 1e-10

    // Compute squared values for current bar
    float error = nz(predicted, 0.0) - nz(actual, 0.0)
    float sqError = error * error
    float sqActual = nz(actual, 0.0) * nz(actual, 0.0)
    float sqPred = nz(predicted, 0.0) * nz(predicted, 0.0)

    // Rolling sums
    float sumSqError = ta.sum(sqError, length)
    float sumSqActual = ta.sum(sqActual, length)
    float sumSqPred = ta.sum(sqPred, length)

    // TheilU = √(Σ(pred-act)²) / √(Σact² + Σpred²)
    float denom = math.sqrt(sumSqActual + sumSqPred)
    float result = denom > epsilon ? math.sqrt(sumSqError) / denom : 0.0
    result

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

// Inputs
i_length = input.int(14, "Length", minval=1)
i_actual = input.source(close, "Actual")
i_predicted = input.source(open, "Predicted")

// Calculation
theilu_value = theil_u(i_actual, i_predicted, i_length)

// Plot
plot(theilu_value, "Theil's U", color=color.yellow, linewidth=2)
hline(0, "Perfect", color=color.green, linestyle=hline.style_dotted)
hline(1, "Naive", color=color.red, linestyle=hline.style_dotted)