ARIMA command + Box Jenkins methodology

Dear community,

In the Matlab article about the Box-Jenkins methodology: http://nl.mathworks.com/help/econ/box-jenkins-model-selection.html

the command 'forecast' is used. It produces yF and yMSE. Then, the confidence intervals are calculated as plus and minus sqrt(yMSE) around yF.

Does this mean that each t^{th} time instance of the forecast is normally (Gaussian) distributed, with mean yF(t) and variance yMSE(t)? How does one know this? Is it based on assumptions?

I studied some basics of ARIMA models on my own, but as you can see still lack some fundamentals.

Thanks, best!

Pieter