Symmetric mean absolute percentage error

Definition

The symmetric mean absolute percentage error (SMAPE) is a measure used to evaluate the accuracy of a forecasting model by calculating the average percentage difference between the forecasted and actual values, while providing a symmetric approach to avoid issues with negative values. It addresses the shortcomings of traditional percentage errors by taking the absolute values and averaging them in a way that treats overestimations and underestimations equally, which makes it particularly useful for models where both types of errors are important.

5 Must Know Facts For Your Next Test

1. SMAPE is calculated using the formula: $$SMAPE = \frac{1}{n} \sum_{t=1}^{n} \frac{|F_t - A_t|}{( |A_t| + |F_t| ) / 2} \times 100$$, where F_t is the forecasted value, A_t is the actual value, and n is the number of observations.
2. One of the key benefits of SMAPE is that it ranges from 0% to 200%, making it easier to interpret compared to other error measures that can be unbounded.
3. SMAPE treats both over-forecasts and under-forecasts equally, ensuring that neither type of error disproportionately affects the accuracy measure.
4. It is especially useful in scenarios where data contains both positive and negative values, as traditional percentage errors can lead to misleading interpretations.
5. SMAPE can be sensitive to small denominator values, leading to inflated error percentages; therefore, it should be applied with caution in datasets with many zero or near-zero actual values.

Review Questions

• How does SMAPE differ from MAPE in its approach to measuring forecast accuracy?
  • SMAPE differs from MAPE in that it uses a symmetric approach for calculating percentage errors. While MAPE only considers absolute differences in predictions relative to actual values, SMAPE includes both forecasted and actual values in its denominator, which allows for equal treatment of overestimations and underestimations. This feature makes SMAPE particularly advantageous when analyzing models that may produce both types of errors, providing a more balanced view of forecasting accuracy.
• In what scenarios would using SMAPE be more beneficial than other forecast accuracy metrics like MAPE?
  • Using SMAPE is more beneficial in scenarios where forecasts may yield both positive and negative values, as it normalizes errors in a way that doesn't favor either direction. For example, in inventory management where stock levels can fluctuate above or below zero, SMAPE offers a clearer picture of overall forecasting performance. Additionally, in datasets where some actual values are close to zero, traditional metrics like MAPE could become misleadingly high, while SMAPE remains more stable and interpretable.
• Evaluate how the properties of SMAPE influence decision-making in business forecasting practices.
  • The properties of SMAPE greatly influence decision-making by providing a clear and balanced measure of forecast accuracy. Businesses can rely on SMAPE to identify whether their forecasting models consistently underperform or overperform without bias toward one type of error. This understanding allows for more informed adjustments to forecasting strategies. Furthermore, since SMAPE offers a bounded scale from 0% to 200%, decision-makers can easily communicate accuracy levels across various stakeholders and make adjustments based on comparative analyses against industry benchmarks.

Related terms

Mean Absolute Percentage Error: Mean Absolute Percentage Error (MAPE) measures the accuracy of a forecasting method by calculating the average absolute percentage error between predicted and actual values.

Forecasting Accuracy: Forecasting accuracy refers to how closely a forecasted value matches the actual outcome, often evaluated using various error metrics such as SMAPE and MAPE.

Absolute Error: Absolute error quantifies the difference between a forecasted value and the actual value without considering the direction of the error, focusing solely on magnitude.