pine files

lib/errors/theilu/theilu.pine

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+// The MIT License (MIT)
+// © mihakralj
+//@version=6
+indicator("Theil's U Statistic", "TheilU", overlay=false)
+
+//@function Calculates Theil's U Statistic (U1)
+//@doc     Relative forecast accuracy measure, normalized RMSE.
+//@doc     U=0: perfect; U=1: naive forecast; U>1: worse than naive.
+//@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)