I've come across some papers in where certain forecast errors are standardized to have unit variance. Unfortunately that's the only information they provide and I have no idea on how to obtain/calculate their results.

Assuming I have a vector of 3 year forecasts that i would like to standardized to have unit variance. I thus calculate the forecast errors such as actual value-forecasted value and get a vector of forecast errors.

I've came up with the following: $x$ equals my forecast errors of the 3 year forecasts


is this correct or would this only be valid for one year forecasts?

  • 2
    $\begingroup$ You don't need to subtract mean(x) unless you also want it to have a mean of 0. Just dividing by the standard deviation will give it unit variance already. $\endgroup$ Aug 17, 2014 at 15:24
  • $\begingroup$ Also: a variable standardized in the way you calculate is often represented with the symbol $z$. ($x-\bar{x}/s_{x}$ is sometimes called the "$z$ transformation", assuming $\bar{x} \approx \mu$, and $s_{x}\approx \sigma_{x}$.) $\endgroup$
    – Alexis
    Aug 17, 2014 at 16:05
  • $\begingroup$ Just in case anyone happens to be confused, Alexis meant to type $(x-\bar x)/s_x$ there. $\endgroup$
    – Glen_b
    Aug 17, 2014 at 16:38
  • $\begingroup$ @Glen_b is a sharp reader as usual. :) I definitely left out the parentheses in my haste. $\endgroup$
    – Alexis
    Aug 17, 2014 at 18:15


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