Loss Functions & DM Test

Two Competing Forecasts

Both forecasts target the same series. Shape their error patterns, then judge which is "better" under different loss functions.

Forecast 1

Bias (mean error) 0.00

Volatility (SD) 1.00

Fat tails (occasional large misses)

Forecast 2

Bias (mean error) 0.00

Volatility (SD) 1.30

Fat tails (occasional large misses)

Loss Function

Squared error (MSE) Absolute error (MAE) Asymmetric (α)

DM Test Settings

Forecast horizon h 1

n = 120 origins · Newey-West bandwidth K = h − 1

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Adjust the sliders to compare forecasts.

Forecast Errors Over Time Forecast 1 Forecast 2

Loss Differential, d(t) = L(e₁ₜ) − L(e₂ₜ)

Error Distributions

Average Loss by Criterion (both forecasts, all three loss functions)