Long-Term Forecast Behavior in Nonstationary ARIMA Models

Summary

The document raises a conceptual question about how long-term forecasts behave for ARIMA models. It contrasts stationary models, whose forecasts are expected to approach a mean, with integrated or otherwise nonstationary specifications, whose forecasts may instead reflect drift. It also asks whether one should difference the data, forecast with a stationary model, and then transform predictions back to the original scale.

The excerpt does not contain a substantive answer to these questions. The response only points to a blog entry and says that long-term forecasts are shown there; the model formulation, forecast paths, and supporting explanation are absent. As a result, this text identifies the issue but does not establish a general convergence rule or explain how differencing, drift, and forecast uncertainty affect long-horizon predictions. Readers would need the referenced material or a fuller treatment to draw conclusions.

Key ideas

• The document asks whether forecasts from nonstationary ARIMA models converge or continue to reflect drift.
• It distinguishes the expected long-run behavior of stationary and nonstationary models.
• It raises differencing and transforming forecasts back to the original scale as modeling considerations.
• The supplied response omits the model setup and explanation needed to resolve the question.

Tags

# ARIMA Forecasting always converges?


# ARIMA Forecasting always converges?












I read an article about arima forecasting and i said that before we forecast arima model, its stationarity has to be checked.

If the model is stationary, it is clear that forecasting converges to whatever the mean the model has.

However for ARIMA(p,d,q) where d>0 or some non-stationary ARIMA(p,0,q), we have to consider a drift of the model and it implies that the model has no convergence in long term.

So, if we want to forecast non-stationary ARIMA model, then do we have to transform to the model to be stationary and proceed forecasting and then transform back to the original data with the calculated forecasting value?

(I know that long-term forecasting using ARIAM is not very useful, but this question is just for understanding the context)

## Answer by Richi Wa (score 1, accepted)

https://quant.stackexchange.com/a/21200

It is too much too text so I take screenshots and the link to Rob Hynman's blog entry:

If you formulate the ARIMA model likes this:

Then you get these long term forecasts:

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.