Fit single ARIMA/ARMA model to multiple independent time series I have approximately 1000 different time series each with a single variable, of length ranging from 5 to 500 periods. They are all independent of each other, and each series can be treated as being generated from the same series generator. The series are stationary. Another way of describing the multiple time series is that they are like a single time series that has "restarted" 1000 times after some number of periods.
How can I fit a single ARIMA model to the entire set of time series?
A previous answer here (Estimating same model over multiple time series) suggests concatenating all the time series with padding in-between to wash out serial correlations. That works okay, but even with large padding the correlations remain and affect the fit and predictions. That is to say, The effect of shocks and the resulting errors in the previous time series is carried through the padding to the next time series - the predicted "starting" value of each time series is not a constant.
Thank you!

Alternatively, per another answer in that thread, you could fit ARIMA models to each series separately (maybe removing the shorter series first). Either let auto.arima() select a model, and then use the model picked for the majority of your time series. Or fit a range of different models to each series and compare their AICs, finally choosing a model with low average AIC (taking a bit of care since AICs are not comparable between series with different orders of integration or seasonal integration). Or per the linked answer, assess models on holdout samples using some comparable metric like MASE, and choosing the model that performs best.
If you want to forecast, you could also use an ensemble of multiple series, e.g., using the $n$ best-performing ARIMA models per one of the approaches above. You could even try estimating weights for the combination, but that often does not improve matters.
