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The problem is that it can be negative (if + <) or even undefined (if + =). Therefore, the currently accepted version of SMAPE assumes the absolute values in the denominator. 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%.
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
The relative change is independent of the unit of measurement employed; for example, the relative change from 2 to 1 m is −50%, the same as for 200 to 100 cm.The relative change is not defined if the reference value (v ref) is zero, and gives negative values for positive increases if v ref is negative, hence it is not usually defined for negative reference values either.
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 .
Mean percentage error; Symmetric mean absolute percentage error; References This page was last edited on 2 April 2024, at 22:32 (UTC). ...
We can therefore use this quotient to find a confidence interval for μ. This t-statistic can be interpreted as "the number of standard errors away from the regression line." Regressions. In regression analysis, the distinction between errors and residuals is subtle and important, and leads to the concept of studentized residuals. Given an ...
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Deviation (statistics) In mathematics and statistics, deviation serves as a measure to quantify the disparity between an observed value of a variable and another designated value, frequently the mean of that variable. Deviations with respect to the sample mean and the population mean (or "true value") are called errors and residuals, respectively.