Should I analyze the residuals of a model selected by auto.arima? I am a PhD student working on time series forecasting using neural
networks and genetic algorithms.
My question is: Is it necessary to analyze the residue, if I use the auto.arima function?
 A: Trust but Verify !You should always be checking the statistical significance of any estimated parameter and evaluating the error process for any remaining structure ( or structure that was injected due to a bad arima model ). This structure could be further arima , pulses , level shifts , seasonal pulses ,local time trends , changes in error variance over time possibly a symptom of changing parameters . deterministic error variance change at one or more points or the need for a Box-Cox transformation. Simple methods (aic/bic) assuming a list of possible models  premise that all of the possible violations are not present. The possible violations should always be tested for by tests on the error process. My first attempt to automate model identification in 1968 was to try some 30 or so models to try and to "pick the best" . That procedure required modification ! 
A: Absolutely! If you want your work to be serious, you should never blindly trust the methods you use. This means analyzing the residuals but also other tests. Always check the validity of your models. There are several reasons for this:

*

*There could be an unknown bug in the third-party software.


*There could be a bug in your own code. Gathering as much information about the model as possible can give you warning signs.


*You may disagree with auto.arima  on what the best model is. It uses its own criteria and you can have yours. Put simply, a "good model" is a compromise between simplicity and precision and there are a lot of valid middle points depending on what your prorities are. Analyzing the residuals of a model could give you a hint on what a reasonable alternative model could look like.


*Sometimes the best model is still not good enough and you need to try an entirely different approach.
