non-normal residuals in ARIMA I am trying to fit an ARIMA model and I have already evaluated a few variations which I finally selected ARIMA(1,1,3) model. The residuals seems to be uncorrelated and all the lags are significant. However, in this model and even in all the others I tried, the normality condition for residuals is always violated and they look like this when plotted against normal distribution. 
Should I transform my data somehow? I have already used natural log and first differencing in order to make the data stationary or can I ignore the assumption when I have a lot of observations (1,5M) ?
 A: Your QQplots could indicate $t$-distributed error terms might fit better. You could try to fit an ARIMA-model with $t$-distributed innovation terms, and see if the fit is very different from the fit you have now. I have done such things with the bugs software, there are certainly other options. 
A: Before you do an ARIMA model you have to check if the data is be stationary and if any seasonality should be defined using autocorrelation (ACF) and partial correlation functions(PACF). The auto correlation should follow the 95% confidence bands. Stationary data is detected using a run sequence plot or auto correlation.
If it is not stationary you might have to detrend it. My guess is it was not stationary.
A: If the residuals contain pulses or level shifts this can lead to "non-normality" . Try detecting Interventions and add them as necessary. Another way residuals can exhibit non-normality is if there is a deterministic change in error variance suggesting Weighted Least Squares OR if the model's parameters are not constant over time suggesting data segmentation..
