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I`m trying to forecast some forex returns of currencies couples. I build up my ARIMA model and test for normality of distribution after the arima is applied. I get different results from the Jarque - Bera Normality Test which p-value is 0.004 < 0.05 and then I should reject the H0 for normality. But when I plot and hist the residuals I see perfectly normal distribution. Where the difference comes from? My data is from 250 observations.

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  • $\begingroup$ Could you plot a normal density with the same mean and variance as your residuals on the same plot? You should be able to see how they differ. $\endgroup$ – Chris Haug Jun 15 at 16:38
  • $\begingroup$ @ChrisHaug There it is my density vs normal one imgur.com/EeM5XMV When you Iook at my plot vs the normal density one we can say that our residuals are normally distributed, their variance is constant over time and they are not correlated, no? Hence I get suprised by the JB test result which rejects normality. That`s how I interpret the rejectting of the H0 : our residuals are not normally distributed -> their variance is not constant over time, we have some data in high kurtosis /skewness and fait tails which is not good for our Arima model. Is that good? $\endgroup$ – Ivan Ar Jun 15 at 23:12

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