// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Tukey's Biweight Loss", "TukeyBiweight", overlay=false)

//@function Calculates Tukey's Biweight (Bisquare) Loss
//@doc     Robust loss that completely rejects outliers beyond threshold c.
//@doc     ρ(x) = (c²/6) * (1 - (1 - (x/c)²)³) for |x| ≤ c; ρ(x) = c²/6 for |x| > c
//@doc     Common c values: 4.685 (95% efficiency), 6.0 (more permissive)
//@param   actual Series of actual values
//@param   predicted Series of predicted/forecast values
//@param   length Rolling window for averaging
//@param   c Threshold for outlier rejection (default 4.685)
//@returns Mean Tukey biweight loss over the window
tukey_biweight(series float actual, series float predicted, simple int length, simple float c = 4.685) =>
    float cSquaredOver6 = (c * c) / 6.0

    // Compute Tukey biweight loss for current bar
    float error = nz(actual, 0.0) - nz(predicted, 0.0)
    float absError = math.abs(error)

    float loss = 0.0
    if absError > c
        loss := cSquaredOver6
    else
        float ratio = error / c
        float ratioSq = ratio * ratio
        float oneMinusRatioSq = 1.0 - ratioSq
        float cubed = oneMinusRatioSq * oneMinusRatioSq * oneMinusRatioSq
        loss := cSquaredOver6 * (1.0 - cubed)

    // Rolling mean of losses
    float result = ta.sma(loss, length)
    result

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

// Inputs
i_length = input.int(14, "Length", minval=1)
i_c = input.float(4.685, "Threshold c", minval=0.1, step=0.1, tooltip="4.685=95% efficiency for normal; 6.0=more permissive")
i_actual = input.source(close, "Actual")
i_predicted = input.source(open, "Predicted")

// Calculation
tukey_value = tukey_biweight(i_actual, i_predicted, i_length, i_c)

// Plot
plot(tukey_value, "Tukey Biweight", color=color.yellow, linewidth=2)
hline(0, "Zero", color=color.gray, linestyle=hline.style_dotted)