How to Calculate MAPE in Forecasting

Mean Absolute Percentage Error, commonly known as MAPE, serves as a widely used metric for evaluating the accuracy of forecasting methods. This statistical measure quantifies the average magnitude of error in a forecast, expressing it as a percentage. It provides a clear, relative indication of how well a forecast aligns with actual outcomes. MAPE is frequently employed due to its straightforward interpretation, making it accessible for understanding forecast performance across various datasets. The metric helps in assessing the precision of predictions by normalizing the error based on the actual values, thereby offering a standardized view of forecasting accuracy.

Prerequisites for Calculation

Calculating the Mean Absolute Percentage Error requires two fundamental sets of data points: actual values and forecast values. Actual values represent the observed, real outcomes that occurred during a specific period. These are the true figures against which the predictions are being measured. Conversely, forecast values are the predicted outcomes generated by a forecasting model or method. These values represent the model’s estimate of what the actual outcomes would be.
The calculation also requires the “absolute error” for each data point, which is the absolute difference between an actual value and its corresponding forecast value.

Step-by-Step Calculation of MAPE

The calculation of Mean Absolute Percentage Error involves several distinct steps to convert individual prediction errors into a single percentage.

• For each data point, determine the absolute error by subtracting the forecast value from the actual value and taking the absolute value of this difference. This ensures the error’s magnitude is considered, regardless of over- or under-prediction.
• Convert each absolute error into a percentage error relative to its actual value. Divide the absolute error by the actual value and multiply by 100. This normalizes the error, making it comparable across different data scales. For example, if the actual value was 100 and the forecast was 95, the absolute error is 5, leading to a percentage error of (5/100)100 = 5%.
• Sum all individual percentage errors.
• Divide this sum by the total number of data points. This yields the mean absolute percentage error across the dataset.

The formula for MAPE is: MAPE = (1/n) Σ (|Actual – Forecast| / Actual) 100, where ‘n’ is the number of data points.

Consider an example with three data points:
1. Actual: 100, Forecast: 95
2. Actual: 120, Forecast: 125
3. Actual: 110, Forecast: 105

For the first point, the absolute error is |100 – 95| = 5, and the percentage error is (5/100)100 = 5%. For the second, the absolute error is |120 – 125| = 5, and the percentage error is (5/120)100 ≈ 4.17%. For the third, the absolute error is |110 – 105| = 5, and the percentage error is (5/110)100 ≈ 4.55%. Summing these percentage errors (5% + 4.17% + 4.55% = 13.72%) and dividing by the number of points (3) results in a MAPE of approximately 4.57%.

Understanding and Applying the MAPE Result

MAPE directly indicates forecast accuracy in percentage terms. A lower MAPE signifies a more accurate forecast, as predicted values are, on average, closer to actual outcomes. For instance, a MAPE of 5% indicates an average forecast deviation of 5% from actual values, while 20% implies a larger deviation and less accuracy.

Organizations use MAPE to compare the performance of different forecasting models. By calculating MAPE for various models, decision-makers can identify which model consistently produces the most reliable predictions. This comparative analysis aids in selecting an optimal forecasting approach, which can lead to better resource allocation or inventory management.

MAPE also helps set performance benchmarks and evaluate forecasting improvements over time. A company might aim to reduce its MAPE from 10% to 7% over a fiscal quarter, reflecting improved forecasting capabilities. This metric helps in understanding the relative magnitude of forecast error, making it suitable for comparing accuracy across different products or time series that may have vastly different scales.

Specific Data Considerations for MAPE

While MAPE offers a clear measure of forecast accuracy, its calculation can encounter specific challenges related to the underlying data. A notable limitation arises when an actual value is zero. Since the MAPE formula involves dividing the absolute error by the actual value, a zero in the denominator leads to an undefined result, making MAPE calculation impossible for that specific data point. This means datasets containing instances of zero actual demand or sales cannot be fully evaluated using standard MAPE.

Another consideration involves very small actual values. When the actual value is extremely small, even a minor absolute error can result in a disproportionately large percentage error. For example, if an actual value is 1 and the forecast is 2, the absolute error is 1, leading to a 100% error. Such occurrences can significantly inflate the overall MAPE, potentially misrepresenting the overall accuracy of the forecast, especially in scenarios with infrequent or low-volume data. Careful consideration of these data characteristics is needed when interpreting MAPE results to avoid misleading conclusions.