Understanding MSE and MARPE
MSE (Mean Squared Error) and MARPE (Mean Absolute Relative Percentage Error) are both metrics used to evaluate the performance of forecasting models. However, they differ in their calculation and interpretation:
- MSE measures the average squared difference between the actual values and the predicted values. It is sensitive to outliers, meaning large errors have a disproportionately large impact on the overall MSE.
- MARPE measures the average percentage difference between the actual values and the predicted values. It is less sensitive to outliers and provides a relative measure of error, making it easier to interpret across different datasets.
Key Differences
Here's a table summarizing the key differences:
| Feature | MSE | MARPE |
|---|---|---|
| Calculation | (Actual - Predicted)^2 | ( |
| Sensitivity to Outliers | High | Low |
| Interpretation | Absolute error in squared units | Relative error in percentage |
| Units | Same as the target variable squared | Percentage |
Practical Insights
- MSE is commonly used in machine learning algorithms where minimizing squared error is the primary objective.
- MARPE is often preferred in business forecasting where understanding the relative error is crucial for decision-making.
Example
Let's say you are forecasting sales for a product. The actual sales were 100 units, and your model predicted 90 units.
- MSE: (100 - 90)^2 = 100
- MARPE: (|100 - 90|/100) * 100 = 10%
This example shows that MSE is a larger value than MARPE, but MARPE provides a more intuitive understanding of the error as a percentage.
Conclusion
Both MSE and MARPE are valuable metrics for evaluating forecasting models. Choosing the appropriate metric depends on the specific application and the desired interpretation of the error.
