# Analyzing residuals vs fitted values in a time series

I fitted a times series using an ARIMA(6,1,0), and tried to analyze the residuals, I wrote a code that gave me same four plots as in the lm R function, the one I'm interested in the last one where I plot residuals against the fitted values, here is the plot there is a clear heteroskedasticity in here right ? Should I use GARCH to get a better fit ?

edit here is how the data plot looks like :

• Not necessarily. What about the outliers? Did you address them? Maybe you should use Tsay's variance test? Maybe you need a deterministic trend variable added to your model? Post your data. – Tom Reilly Jun 30 '16 at 18:25
• Thank you for your answer, I used the package tsoutliers and didn't any outlier detected. Can you explain more how to implement a deterministic trend variable ? I can't post the data (i posted the time series plot) – Mohamed Nidabdella Jul 1 '16 at 7:23
• Scale the data - Multiply all the data by any number. It's still the same dataset, but now deidentified. Tsoutliers is a nice package, but it is not complete. – Tom Reilly Jul 1 '16 at 12:53
• There clearly are some patterns in your residuals, indicating that the fitted model does not account for all that the data has to tell. What kind of data is that? What are you trying to model? Judging from the graphs, adding a GARCH structure for the error variance is unlikely to fix the problem. – Richard Hardy Jul 8 '16 at 14:23