Is there a simple formula to find the MAPE for $Y_t$ if we know the MAPE for $\Delta$log($Y_t)$ ~ iid N($\mu$,$\sigma^2$)?
Is there an algebraic relation between the two?
What if I use RMSFE instead? Or some other measure of forecast accuracy.
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$\begingroup$ If there is a formula it is certainly not simple. Furthermore MAPE is a very bad fit statistic for $\Delta\log(Y_t)$, since you should have a sizeable amount of values close to zero, which should make MAPE large. Also do you claim that MAPE is normal, or $\Delta\log(Y_t)$ is normal? $\endgroup$– mpiktasCommented Jan 6, 2014 at 9:24
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$\begingroup$ I assume $\Delta log(Y_t)$ is normal. $\endgroup$– ChristianCommented Jan 6, 2014 at 10:07
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$\begingroup$ That's a good point mptikas, I did not think of that $\endgroup$– ChristianCommented Jan 6, 2014 at 10:09
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$\begingroup$ Moreover, I just thought recently that it is a bit weird that I'm using MAPE if I'm interested in minimising MSE loss. But I'm not sure if that's relevant to this question. Just a thought. $\endgroup$– ChristianCommented Jan 6, 2014 at 10:10
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$\begingroup$ Ok, suppose your data follows normal distribution. But MAPE is calculated using fit from some model and you did not tell what model is that. If you have the data and the model, then simply transform back to levels and then calculate MAPE. And yes if you minimise MSE, MAPE is probably not what you want. Although it gives some idea about the fit, it is not best statistic for forecast accuracy. $\endgroup$– mpiktasCommented Jan 6, 2014 at 13:19
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