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I'm working with a VAR model to do forecast involving two non-stationary time series (quarterly frequency). The literature indicates to verify if there is cointegration and, otherwise, to use the differentiation to reach stationarity.

I did a forecast for 4 periods ahead with the stationary series in differences and other with the series in level. The model with series in level presented a better performance, ie, a smaller RMSE.

This bothered me with the fact of non-stationarity, but then I found this comment here https://stats.stackexchange.com/a/192165/200303 which says that non-stationarity is not necessarily a problem in the case of VAR model forecasting.

Is this right? Could you point me papers or books that comment on this, which show this flexibility?

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