Published by: Dikshya
Published date: 24 Jul 2023
Introduction:
Forecast accuracy is a crucial aspect of evaluating the performance of predictive models and forecasting techniques. It helps us understand how well a forecast model predicts future values compared to the actual observed values. Several metrics are commonly used to measure forecast accuracy, including Mean Absolute Deviation (MAD), Mean Absolute Percentage Error (MAPE), and Mean Squared Error (MSE). Each of these metrics provides unique insights into the accuracy and reliability of the forecasts.
1. Mean Absolute Deviation (MAD):
MAD is a simple and intuitive measure of forecast accuracy that quantifies the average absolute difference between the forecasted values and the actual observed values. It measures the magnitude of forecast errors without considering their direction. MAD is calculated using the following formula:
MAD = Σ |(Actual - Forecast)| / n
where:
A lower MAD indicates better forecast accuracy, as it means the forecasted values are closer to the actual values.
2. Mean Absolute Percentage Error (MAPE): MAPE is a percentage-based metric that measures the accuracy of forecasts relative to the magnitude of the actual values. It calculates the average percentage difference between the forecasted values and the actual observed values. MAPE is given by the following formula:
MAPE = (Σ |(Actual - Forecast)| / Σ Actual) * 100 / n
where:
MAPE is particularly useful when you want to understand the forecast accuracy in percentage terms and when dealing with data of varying scales. Like MAD, a lower MAPE indicates better forecast accuracy.
3. Mean Squared Error (MSE): MSE is another popular metric used to measure forecast accuracy. It considers both the magnitude and direction of forecast errors by squaring the differences between the forecasted values and the actual observed values. MSE is calculated using the following formula:
MSE = Σ (Actual - Forecast)^2 / n
where:
MSE penalizes large errors more than smaller errors due to the squaring operation. Unlike MAD and MAPE, MSE is not in the same unit as the original data, making it harder to interpret.
Conclusion:
Each of the measures of forecast accuracy - MAD, MAPE, and MSE - has its strengths and limitations. MAD and MAPE are easier to interpret and are suitable for comparing forecast accuracy across different datasets. MSE, on the other hand, gives greater weight to larger errors and is commonly used in optimization problems for model fitting. When evaluating forecast accuracy, it's essential to consider the specific characteristics of the data and the goals of the forecasting task to choose the most appropriate metric. Additionally, it is good practice to use multiple metrics to gain a comprehensive understanding of the forecasting model's performance.