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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.
A percentage change is a way to express a change in a variable. It represents the relative change between the old value and the new one. [6]For example, if a house is worth $100,000 today and the year after its value goes up to $110,000, the percentage change of its value can be expressed as = = %.
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%.
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.
MAPE puts a heavier penalty on negative errors, < than on positive errors. [9] As a consequence, when MAPE is used to compare the accuracy of prediction methods it is biased in that it will systematically select a method whose forecasts are too low.
It is remarkable that the sum of squares of the residuals and the sample mean can be shown to be independent of each other, using, e.g. Basu's theorem.That fact, and the normal and chi-squared distributions given above form the basis of calculations involving the t-statistic:
This approximate formula is for moderate to large sample sizes; the reference gives the exact formulas for any sample size, and can be applied to heavily autocorrelated time series like Wall Street stock quotes. Moreover, this formula works for positive and negative ρ alike. [12] See also unbiased estimation of standard deviation for more ...
The false positive rate (FPR) is the proportion of all negatives that still yield positive test outcomes, i.e., the conditional probability of a positive test result given an event that was not present. [6] The false positive rate depends on the significance level. The specificity of the test is equal to 1 minus the false positive rate.