Calculate RMSE from Time-Series Model Predictions

Consider a financial analyst who has developed a time-series model predicting monthly stock returns based on historical data. After fitting the model, the analyst wants to evaluate its predictive accuracy by comparing the model predicted values against the actual observed values over the last 12 months.

To assess the model's performance, the analyst calculates the Mean Squared Error (MSE) and the Root Mean Squared Error (RMSE). The observed returns for the last 12 months and the corresponding predicted returns are as follows:

• Month 1: Actual: 0.03, Predicted: 0.025
• Month 2: Actual: 0.04, Predicted: 0.035
• Month 3: Actual: 0.02, Predicted: 0.015
• Month 4: Actual: 0.01, Predicted: 0.005
• Month 5: Actual: -0.02, Predicted: -0.015
• Month 6: Actual: 0.01, Predicted: 0.012
• Month 7: Actual: 0.03, Predicted: 0.033
• Month 8: Actual: 0.05, Predicted: 0.045
• Month 9: Actual: 0.04, Predicted: 0.038
• Month 10: Actual: 0.02, Predicted: 0.018
• Month 11: Actual: -0.01, Predicted: -0.012
• Month 12: Actual: 0.00, Predicted: -0.005

Using this data, what is the RMSE of the model?