I am doing a time series analysis and the Augmented-Dickey Fuller Test result says that my data is stationary. But my raw data is not normally distributed. When I took the first difference of my data, it is now normally distributed. Is it okay to use the first differentiated data even though my raw data is stationary from the start?

  • $\begingroup$ Why do you want to do that? You probably need a very good reason, overdifferencing is usually a troublemaker. $\endgroup$ – kjetil b halvorsen Nov 30 '16 at 12:50
  • $\begingroup$ The ARIMA models generated by the not differentiated data has a small R-squared (from -0.626 to 0.159) and its residuals do not satisfy the assumption of normality and correlation. While the differentiated one provided models with higher R-squared (from 0.178 to 0.304) and there is a model that satisfies all the assumption for its residual. $\endgroup$ – Angel S. Nov 30 '16 at 13:06
  • $\begingroup$ I don't think you should differentiate to get normal residuals. How did you get an R²-of -0.626? $\endgroup$ – kjetil b halvorsen Nov 30 '16 at 13:19
  • $\begingroup$ Here is the Estimation Output of MA(1) model generated using E-views 9: i.stack.imgur.com/Y14Ag.png $\endgroup$ – Angel S. Nov 30 '16 at 14:01

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