Explanation

When comparing out-of-sample forecasting performance, Root Mean Squared Error (RMSE) is the most appropriate metric because:

• RMSE measures the average magnitude of forecasting errors, with larger errors being penalized more heavily due to squaring
• It directly assesses predictive accuracy on unseen data
• Lower RMSE values indicate better forecasting performance

Why other options are incorrect:

• $R^2$: Measures in-sample goodness of fit, not out-of-sample predictive accuracy
• Durbin-Watson statistic: Tests for autocorrelation in residuals, not forecasting performance

For time series forecasting model comparison, RMSE is the standard metric for evaluating out-of-sample predictive accuracy.