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This little-known but serious issue can be overcome by using an accuracy measure based on the logarithm of the accuracy ratio (the ratio of the predicted to actual value), given by (). This approach leads to superior statistical properties and also leads to predictions which can be interpreted in terms of the geometric mean.
Mean directional accuracy (MDA), also known as mean direction accuracy, is a measure of prediction accuracy of a forecasting method in statistics. It compares the forecast direction (upward or downward) to the actual realized direction. It is defined by the following formula:
One supposed problem with SMAPE is that it is not symmetric since over- and under-forecasts are not treated equally. The following example illustrates this by applying the second SMAPE formula: Over-forecasting: A t = 100 and F t = 110 give SMAPE = 4.76%; Under-forecasting: A t = 100 and F t = 90 give SMAPE = 5.26%.
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A forecast bias occurs when there are consistent differences between actual outcomes and previously generated forecasts of those quantities; that is: forecasts may have a general tendency to be too high or too low. A normal property of a good forecast is that it is not biased.
where is the actual value of the quantity being forecast, is the forecast, and is the number of different times for which the variable is forecast. Because actual rather than absolute values of the forecast errors are used in the formula, positive and negative forecast errors can offset each other; as a result, the formula can be used as a ...
If the forecast is 100% (= 1) and it rains, then the Brier Score is 0, the best score achievable. If the forecast is 100% and it does not rain, then the Brier Score is 1, the worst score achievable. If the forecast is 70% (= 0.70) and it rains, then the Brier Score is (0.70−1) 2 = 0.09.
Michael Fish - A few hours before the Great Storm of 1987 broke, on 15 October 1987, he said during a forecast: "Earlier on today, apparently, a woman rang the BBC and said she heard there was a hurricane on the way.