Is there any reason why recursive forecasts cannot be included in the ARIMA option for univariate modelling together with their confidence intervals when the model is truly univariate with no exogenous varisbles included in the specification  Clearly post sample data the MA terms would drop out of the forecasts that would effectively only require the AR parameters and any differencing.

I'm wondering whether what you're trying to achieve is the same thing as what's called "recursive" in gretl. Maybe it is, but the terminology can be complex and not always universal.

So: If you have a base sample from t=T1 to t=T2, and you estimate your Arima model on that sample, and then you want to create forecasts for the out-of-sample range T2+1 through T2+h, for a certain positive integer h, you can do that, but we wouldn't call it recursive. Example:

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This is a forward-iterated forecast. Again, maybe this is _not_ what you're actually trying to do, I just want to make sure there are no misunderstandings, because sometimes people call this thing recursive.

In contrast, what gretl calls "recursive" --and I hope I'm getting this right-- entails updating/re-estimating the model coefficients for every new value, starting from very early in the original base sample. So T2 is not fixed anymore (and this could become computationally expensive for non-OLS estimators). Example:

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I'm noticing that the printout here has no values for the final two observations - to be honest, I don't know why that is so, all the necessary ingredients should be there. Can anybody explain this, please?

thanks

sven