ARIMA(1,1,1) model doesn't seem to discard non-differentiated values after differentiation.

[enriicoo]

ARIMA(1,1,1) model doesn't seem to discard non-differentiated values after differentiation.

[ChadFulton]

Yes, I agree that we should probably change our behavior here to report NaN values.

The reason it is the way it is currently is that for the specified model, the "forecast" for the first period is equal to zero, so the forecast error is equal to the first value. Obviously that is not very useful. In addition, although technically the point forecast is equal to zero, it comes from a diffuse prior and the zero is arbitrary, so reporting the forecast error doesn't really make sense from that perspective either.

[ChadFulton]

Note that these warnings:

UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "

are not related to the same issue as the first forecast error.

[enriicoo]

I've got no experience on the algorithms that make the timeseries models, but these warnings aren't raised when I make the same model in R and Gretl. I would like to understand the nature of these warnings and best ways of solving them. I have to note I know it's a suboptimal sample (n<30) and it might as well have something to do with that.