Forecasting with autocorrelation present

#1
Hello, if one is to compare different lag orders for forecasting (and minimize RMSFE, root mean squared forecast error) for lets say autoregressive models and the datagenerating process is an AR(4) model. Thereby using an AR(3) model to forecast one should expect worse RMSFE values than an AR(4) model, but for the sake of discussion, lets say that AR(3) yielded a lower RMSFE although the bias introduced by remaining autocorrelation. Could one then say that the AR(3) is more preferable since the RMSFE is lower even if the AR(4) better fullfils regression assumptions? In other words, can one say that the autocorrelation in AR(3) does not matter when chosing the optimal model since RMSFE is all that matters?

(My real model would be a vector autoregressive model but I use an AR model in this discussion to simplify)
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
Well you want to meet your assumptions and best fit the true underlying functional form. Sometime in statistictics you can get what look like better fit statistic via model mispecification, but you need to make a judgement call towards the true form.

I am not overly experienced with forecasting, but I wonder how they both look via time series graphs and whether the rsme differences are actually contextually significant.