// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Pseudo-Huber Loss", "PseudoHuber", overlay=false)

//@function Calculates Pseudo-Huber Loss (Charbonnier Loss)
//@param   actual Series of actual values
//@param   predicted Series of predicted/forecast values
//@param   length Rolling window for averaging
//@param   delta Scale parameter controlling transition smoothness (default 1.0)
//@returns Mean Pseudo-Huber loss over the window
pseudohuber(series float actual, series float predicted, simple int length, simple float delta = 1.0) =>
    float deltaSquared = delta * delta

    // Compute Pseudo-Huber loss for current bar: δ² * (√(1 + (error/δ)²) - 1)
    float diff = nz(actual, 0.0) - nz(predicted, 0.0)
    float ratio = diff / delta
    float sqrtTerm = math.sqrt(1.0 + ratio * ratio)
    float loss = deltaSquared * (sqrtTerm - 1.0)

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

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

// Inputs
i_length = input.int(14, "Length", minval=1)
i_delta = input.float(1.0, "Delta (transition scale)", minval=0.001, step=0.1, tooltip="Controls transition between quadratic and linear behavior")
i_actual = input.source(close, "Actual")
i_predicted = input.source(open, "Predicted")

// Calculation
pseudohuber_value = pseudohuber(i_actual, i_predicted, i_length, i_delta)

// Plot
plot(pseudohuber_value, "Pseudo-Huber", color=color.yellow, linewidth=2)
hline(0, "Zero", color=color.gray, linestyle=hline.style_dotted)