Root Mean Square Error (RMSE) is a commonly used metric in time series forecasting that measures the average magnitude of the forecasting errors. It is computed by taking the square root of the average of the squares of the errors—that is, the differences between predicted values and actual values. Essentially, RMSE quantifies how well a forecasting model performs by providing a single numerical value that represents the model's error. A lower RMSE value indicates better model accuracy, as it signifies that the predicted values are closer to the actual values.
To calculate RMSE, you begin by taking the difference between each predicted value and its corresponding actual value, squaring those differences, and then averaging the squared values over the total number of forecasts. Finally, you take the square root of this average to get the RMSE. For example, consider a scenario where you forecasted temperatures for a week and recorded actual temperatures. If your forecasted values were 30°C, 32°C, and 29°C, and the actual temperatures were 31°C, 30°C, and 28°C, the individual errors would be 1°C, 2°C, and 1°C. Squaring these errors gives you 1, 4, and 1, which you would average and then take the square root of to find the RMSE.
RMSE is particularly useful in comparing different forecasting models or assessing improvements in a model. However, it is essential to note that RMSE is sensitive to outliers because it squares the errors, giving more weight to larger discrepancies. This sensitivity means that if there are significant outliers in your data, the RMSE might not accurately reflect the model's performance on the majority of the dataset. As a result, while RMSE is a valuable tool, it can be beneficial to use it in conjunction with other metrics like Mean Absolute Error (MAE) or Mean Absolute Percentage Error (MAPE) for a more comprehensive evaluation of forecasting accuracy.