ARIMA vs. Smoothing Models for Forecasting

Question

I am working with a Renewable Energy customer who wants to create forecasts of energy over time for wind and solar plants.  I was planning to show ARIMA, but then started tinkering with Smoothing models.  Which one is better in your opionion for forecasting?  The advantage I see with ARIMA is the input function.  But if there is no input, is Smoothing better?  I created models with both on Airline Passenger volume data that I believe came from @jiancao.  The AIC was better with the ARIMA model I choose, but the diffence in the predicted values & actual was smaller with the Winters Method.  Thoughts?

JerryFish · Accepted Answer

Alisa, my thought is that it's like other models in JMP... Which is best?  It depends!  Is the improvement in Rsqd/AIC/BIC/... enough to warrant slightly better predictions, or is a simpler (i.e. easier to explain) model better, at the expense of a little prediction ability?

I've had a little experience with ARIMA over the years (though I'm no expert), and I find it pretty good at predictions, but difficult to explain what's going on behind the scenes.  Some of the smoothing models are much easier to explain.

You probably already know this, but for Time Series the equivalent of the "validation column" used in most other platforms is to hold out the last few points in the series, fit the model, then see how well it fits those last few points.  Then you might pick the model that does the best for those points, and go back and refit the same model complexity with those points included (so you are ready to forecast the next model).

Does that help at all?

jiancao · Accepted Answer

I agree with Jerry about using "leave-one-out' as validation in forecasting models. I'd like to add additional comments regarding comparing ARIMA with smoothing models based on AIC.

There are some equivalence relationships for the ARIMA and smoothing models, but they are considered two different families of models.Therefore, AIC cannot be used to compare between them because the likelihood is computed in different ways. In other words, we can only use AIC to select an ARIMA model between candidate ARIMA models or an smoothing model between candidate smoothing models.

Smoothing methods are appealing because they model directly the components of a time series: level, trend, seasonality and random fluctuations, 
They provide quick and simple forecasting without having to develop a model. On the other hand, ARIMA models may produce more accurate forecasts and confidence intervals, but they require more time and input from users.

(BTW, the airline passenger data is from Box and Jenkins's book and can be found in the JMP Sample Data Library's Time Series subfolder, called Seriesg. )