Estimate single ARIMA for multiple timeseries

Question

I have two groups of time-series, each group represents one type of data. However within each group, each time series may be fitted with a different ARIMA(p,d,q) from the other time series in the same group.

I need to create a single model for each group (Model_group1, Model_group2). I tried the approach mentioned by Rob Hyndman in: Estimating same model over multiple time series.

I need to use these two models to classify any time series to one of these two groups. For each time series, I calculated the AIC of Model_group1 and Model_group2, and the model with smaller AIC will mean that the time series belongs to its corresponding group.

I have three problems:

1. I received a warning message

   Series: ts 
   ARIMA(3,0,2) with non-zero mean 
   
   Coefficients:
            ar1     ar2     ar3     ma1      ma2  intercept
         0.0714  0.1417  0.0000  0.0893  -0.0871     0.1169
   s.e.     NaN  0.1381  0.0127     NaN   0.1436     0.0026
   
   sigma^2 estimated as 0.2202:  log likelihood=-33822.63
   AIC=67659.26   AICc=67659.26   BIC=67725.99
   Warning message:
   In sqrt(diag(x$var.coef)) : NaNs produced
   

   This message was returned by only one of the group models. Does that mean that the fitted model is not correct?

2. I got two different results using

   auto.arima(ts, allowdrift=FALSE, stepwise=FALSE)
   auto.arima(ts, allowdrift=FALSE, stepwise=TRUE)
   

3. When I tested the resulting models, the majority of the time-series were classified as group_1, even when I test one of the time series used to build the long time series of group_2. I need to mention here that the composed time series of group_1 is quite shorter than the time series of group_2. Are there any expected reasons for that?

Answer 1

1. That can happen when the model is not suitable for the data.

2. stepwise=FALSE makes auto.arima work harder to find the best model. So of course, sometimes it finds a different model than when stepwise=TRUE.

3. It is impossible to say with the information provided. You should be aware that comparing AIC values with different values of $d$ is inappropriate. The AIC can only be used to compare models with the same $d$.