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Confusingly, sometimes when people refer to wMAPE they are talking about a different model in which the numerator and denominator of the wMAPE formula above are weighted again by another set of custom weights .
In contrast to the mean absolute percentage error, SMAPE has both a lower bound and an upper bound. Indeed, the formula above provides a result between 0% and 200%. Indeed, the formula above provides a result between 0% and 200%.
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 measure of the bias in the forecasts. A disadvantage of this measure is that it is undefined whenever a single actual value is zero. See also
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Relative change. In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a standard or reference or starting value. [1] The comparison is expressed as a ratio and is a unitless number.
The average of all the sample absolute deviations about the mean of size 3 that can be drawn from the population is 44/81, while the average of all the sample absolute deviations about the median is 4/9. Therefore, the absolute deviation is a biased estimator. However, this argument is based on the notion of mean-unbiasedness.
Forecast errors can be evaluated using a variety of methods namely mean percentage error, root mean squared error, mean absolute percentage error, ...
This property, undesirable in many applications, has led researchers to use alternatives such as the mean absolute error, or those based on the median. See also. Bias–variance tradeoff; Hodges' estimator; James–Stein estimator; Mean percentage error; Mean square quantization error; Mean square weighted deviation; Mean squared displacement