Hidden Table: LINK_POOL
| Anchor Text | Internal URL Slug |
|---|---|
| Forecast accuracy | forecast_accuracy |
| Time series | time_series |
| Regression analysis | regression_analysis |
| Data points | data_points |
| Residuals | residuals |
| Statistical bias | statistical_bias |
| Outliers | outliers |
| Economic forecasts | economic_forecasts |
| Performance metrics | performance_metrics |
| Quantitative analysis | quantitative_analysis |
| Error measurement | error_measurement |
| Financial modeling | financial_modeling |
| Prediction | prediction |
| Absolute deviation | absolute_deviation |
| Financial metrics | financial_metrics |
What Is Mean Absolute Percentage Error?
Mean Absolute Percentage Error (MAPE) is a statistical measure used in financial modeling and forecasting to quantify the accuracy of a predictive model. It expresses the average magnitude of error as a percentage of the actual values. As a key concept within Financial Modeling & Forecasting, MAPE provides an intuitive understanding of how far off predictions are, on average, from the observed outcomes. This performance metric is particularly useful because it presents error in relative terms, making it easier to compare forecast accuracy across different datasets or series with varying scales.
History and Origin
The Mean Absolute Percentage Error (MAPE) emerged as a practical error measurement tool, gaining popularity due to its interpretability in percentage terms. Its origins are not attributed to a single inventor but rather evolved as a natural extension of other absolute error metrics, providing a relative measure of forecast accuracy. By expressing errors as a percentage, MAPE offered a clear, unit-free way to assess prediction performance, making it highly appealing in various applied fields, including business and economics. The use of MAPE as a quality measure for regression analysis models has been a subject of academic study, highlighting its role in evaluating predictive performance.9
Key Takeaways
- Mean Absolute Percentage Error (MAPE) measures the average absolute percentage difference between forecasted and actual values.
- It provides a relative measure of forecast accuracy, expressed as a percentage, making it easy to understand and compare across different contexts.
- MAPE is widely used in various fields, including business, economics, and finance, for evaluating predictive models and economic forecasts.
- A lower MAPE value indicates higher accuracy, with 0% signifying a perfect forecast.
- Despite its intuitive appeal, MAPE has limitations, especially when actual values are zero or very close to zero, or when actual values are small.
Formula and Calculation
The Mean Absolute Percentage Error (MAPE) is calculated by taking the average of the absolute percentage errors for each data point. The formula for MAPE is:
Where:
- ( n ) = The number of fitted points (observations)
- ( A_t ) = The actual value at time ( t )
- ( F_t ) = The forecast (predicted) value at time ( t )
- ( | \cdot | ) = Denotes the absolute value
- ( \sum ) = Summation over all observations
To calculate MAPE, the absolute difference between the actual value and the forecast value is first determined for each observation. This absolute deviation is then divided by the actual value to convert it into a percentage error. Finally, these individual percentage errors are summed, and their average is taken to arrive at the overall MAPE.
Interpreting the Mean Absolute Percentage Error
Interpreting the Mean Absolute Percentage Error is straightforward: the resulting percentage represents the average magnitude of the forecast error relative to the actual observed values. For instance, a MAPE of 10% means that, on average, the predictions deviate by 10% from the actual outcomes. A lower MAPE indicates a more accurate model, with 0% MAPE representing a perfect forecast where predicted values exactly match actual values.
However, context is crucial when evaluating a MAPE value. What constitutes an "acceptable" MAPE varies significantly by industry, the type of data being forecasted, and the volatility of the underlying time series. For highly stable data, a MAPE of 5% might be considered high, while for volatile market data, a MAPE of 20% could be acceptable. Analysts often use MAPE in conjunction with other financial metrics to gain a comprehensive understanding of model performance.
Hypothetical Example
Consider a financial analyst forecasting the quarterly earnings per share (EPS) for a company over four quarters.
| Quarter | Actual EPS (( A_t )) | Forecast EPS (( F_t )) | Absolute Error ( |A_t - F_t| ) | Percentage Error ( \left| \frac{A_t - F_t}{A_t} \right| \times 100% ) |
| :------ | :-------------------- | :-------------------- | :----------------------------- | :------------------------------------------------------------------ |
| Q1 | $1.20 | $1.14 | $0.06 | ( \frac{0.06}{1.20} \times 100% = 5% ) |
| Q2 | $1.50 | $1.60 | $0.10 | ( \frac{0.10}{1.50} \times 100% = 6.67% ) |
| Q3 | $1.10 | $1.05 | $0.05 | ( \frac{0.05}{1.10} \times 100% = 4.55% ) |
| Q4 | $1.80 | $1.75 | $0.05 | ( \frac{0.05}{1.80} \times 100% = 2.78% ) |
To calculate the Mean Absolute Percentage Error for these forecasts:
In this hypothetical example, the Mean Absolute Percentage Error for the EPS forecasts is 4.75%. This indicates that, on average, the analyst's quarterly EPS predictions were off by 4.75% from the actual reported earnings.
Practical Applications
Mean Absolute Percentage Error finds widespread practical applications across various sectors of finance and economics where accurate quantitative analysis and forecasting are critical.
- Financial Forecasting: Investment banks, asset management firms, and corporate finance departments use MAPE to assess the accuracy of models predicting stock prices, revenue, expenses, and other financial variables. For example, a company might use MAPE to evaluate the precision of its sales forecasts, directly impacting inventory management and production planning.
- Economic Analysis: Central banks, governmental agencies, and international organizations like the International Monetary Fund (IMF) utilize MAPE to evaluate the accuracy of their economic forecasts for GDP growth, inflation, and unemployment. While such forecasts may miss actual outcomes, MAPE helps quantify the average magnitude of these misses. For instance, the IMF's short-term forecasts for GDP growth and inflation have generally been unbiased, but their accuracy is comparable to private forecasts and can be less reliable during recessions.8,7 Forecasts from sources such as Reuters polls also demonstrate how economic activity can miss analyst calls, highlighting the real-world utility of error metrics like MAPE.6
- Retail and Supply Chain: Businesses in retail often use MAPE to gauge the accuracy of demand forecasts, which directly influences supply chain efficiency, inventory levels, and ultimately, profitability.
- Risk Management: In financial risk management, MAPE can be employed to evaluate the performance of models that forecast market volatility or potential losses, helping institutions to better prepare for adverse events.
Limitations and Criticisms
Despite its intuitive appeal and widespread use, the Mean Absolute Percentage Error (MAPE) has several notable limitations and criticisms that analysts should consider.
One significant drawback is its behavior when actual values (( A_t )) are zero or very close to zero. In such cases, the denominator in the MAPE formula approaches zero, causing the percentage error to become undefined or excessively large, potentially distorting the overall average.5, This issue can make MAPE unsuitable for datasets with frequent zero values, such as demand for intermittent products or new, low-volume financial instruments.
Another criticism is MAPE's inherent statistical bias. It tends to penalize negative errors (over-forecasts) more heavily than positive errors (under-forecasts) of the same absolute magnitude. For example, if the actual value is 100 and the forecast is 50 (a 50% under-forecast), the absolute percentage error is 50%. However, if the actual value is 50 and the forecast is 100 (a 100% over-forecast), the absolute percentage error is 100%. This asymmetry can incentivize models to under-forecast to achieve a lower MAPE.4
MAPE can also be sensitive to outliers or extreme values, especially if those outliers are actual values close to zero, as previously mentioned. This sensitivity can lead to a misleading representation of the model's true accuracy.3,2 Because of these limitations, alternative or complementary performance metrics are often recommended, particularly when dealing with data that exhibits zeroes, small values, or significant volatility. Research has explored the consequences of using MAPE for regression models and suggests that it effectively translates to a weighted Mean Absolute Error (MAE) regression, with weights inversely proportional to the actual values.1
Mean Absolute Percentage Error vs. Mean Absolute Error
The Mean Absolute Percentage Error (MAPE) and Mean Absolute Error (MAE) are both popular metrics for assessing the accuracy of forecasts, but they differ fundamentally in their interpretation and application.
| Feature | Mean Absolute Percentage Error (MAPE) | Mean Absolute Error (MAE) |
|---|---|---|
| Units | Expressed as a percentage, making it unit-free. | Expressed in the same units as the original data. |
| Interpretation | Represents the average absolute percentage deviation of forecasts from actuals. Easier for non-experts to understand relative accuracy. | Represents the average absolute magnitude of the errors. Provides a clear understanding of error size in actual terms. |
| Sensitivity to Scale | Scale-independent; useful for comparing forecasts across different series with varying magnitudes. | Scale-dependent; not ideal for comparing accuracy across vastly different scales without additional context. |
| Zero Values | Problematic when actual values are zero or near-zero, leading to undefined or extremely large errors. | Not affected by zero or near-zero actual values. |
| Bias | Tends to be biased towards under-forecasting due to asymmetric penalization of errors. | Does not inherently bias forecasts towards over or under-prediction. |
While MAPE offers an intuitive percentage-based view of accuracy, MAE provides a more direct measure of error in the original units of the data. The choice between MAPE and MAE often depends on the specific context of the forecasting problem, the characteristics of the data, and the target audience for the forecast accuracy assessment.
FAQs
Why is Mean Absolute Percentage Error useful?
Mean Absolute Percentage Error is useful because it expresses forecast errors as a percentage, providing a relative measure of accuracy that is easy to interpret and compare across different datasets, even if they have vastly different scales. This makes it highly accessible for stakeholders who may not be experts in quantitative analysis.
Can Mean Absolute Percentage Error be negative?
No, Mean Absolute Percentage Error (MAPE) cannot be negative. The formula for MAPE involves taking the absolute deviation of the error and then dividing by the actual value before summing and averaging. This ensures that all individual percentage errors are positive, resulting in a positive or zero MAPE value.
What is a good MAPE value?
What constitutes a "good" Mean Absolute Percentage Error (MAPE) value is highly context-dependent. There is no universal benchmark. For some highly predictable time series (e.g., stable sales data), a MAPE of less than 5% might be considered excellent. For more volatile data, such as stock prices or certain economic forecasts, a MAPE of 15% or even 20% might be considered acceptable. The ideal MAPE should be evaluated in comparison to industry standards, historical performance, and the specific objectives of the forecast.