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In my time series course at uni we were taught to always use a Jarque-Bera test to test if the residuals of any analysis are normally distributed. But what do we need normally distributed residuals for? From my understanding the normality would assure that the conditional expected value of the error term is zero and that the residuals are homoskedastic. But Heteroskedasticity is not a big problem - we could just use robust SEs - and the residuals might not be normally distributed while the conditional expected value of the error term is zero nevertheless. So why do we care about normality?

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  • $\begingroup$ It depends very much on what kind of heteroskedasticity is present, ex. if you residuals are not distributed around the mean (say they have a polynomial looking shape) then even robust SE won't help and will give you wrong inference. $\endgroup$ Jul 13, 2020 at 8:47

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