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Example: I've got an forecast with 2000 values. Let's say they are for one year. I can group my values into months. Every month can include a different number of single values. (JAN with 200 values + FEB with 150 values + ... = 2000 values for the year )

There are two ways of calculating an error:

A) 1. Calc the errors of single values 2. Mean of this Errors (n=2000) -> Gives me the mean error, that i should use to talk about the forecast accuracy.

But what information do i get using the following way:

B) 1. Mean of the single values per month (n = various) 2. Calc the error of the mean per month 3.) Sum up the mean again (n=12)

Would it be the same?

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The two will not be the same in general.

A) is the simple average where all of your 2000 observations has the same impact on the mean

B) is more like the weighted average, where the observations tend to get larger weights in month with smaller sample sizes.

The interpretation is also very different: A) is about the expected errors for any forecast deviating the population mean and B) is about the average errors deviating from the monthly mean.

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