# How far ahead are ARIMA and Exponential smoothing useful?

Are there pragmatic bounds on how far ahead one can use an ARIMA or Exponential Smoothing forecast? I have 2 years of weekly data, yet the problem I am trying to solve requires a forecast that is 12 months out.

I'm thinking that a simple average of the LY and LLY data:

TS(week 44 year 3) = [TS(week 44 year 2) + TS(week 44 year 1)]/2


would be just a good a guess as whatever ARIMA or ETS would give me.

Is this indeed a more pragmatic approach than a more involved forecasting method?

Some of the data show a potential year to year trend, but are two years enough to decide that the TS is trending in a given direction ?

• The further ahead in time you forecast the less accurate any good forecasting method will be. The question really is what is the best model that fits the past data. – Michael R. Chernick Dec 15 '16 at 3:29
• Just calculate prediction intervals from the model and data, then you can see for yourself, and do not need a simple rule-of-thumb. – kjetil b halvorsen Dec 15 '16 at 9:49
• I have recently studied thousands of monthly time series of lengths between 1 and 84 months. Wherever possible I fit three models: univariate, regression on date (including two sinusoidal terms), and additive seasonal Holt-Winters (ETS). The HW method frequently works well to forecast the next full year provided at least three full seasons (years) of data are available. The reason is obvious: you need to estimate the individual seasonal terms with some reliability. One or two years would not be sufficient. Only 18 months tend to suffice to estimate a trend in the regression model. – whuber Jan 11 '17 at 22:29
• @whuber Do you have this study you talk about published / written in a paper? Or perhaps got a recommendation for a similar one? Am interested in it as I will soon start building forecasting models based on 3 years of weekly data to predict 3 months in the future (and possibly up to 1 year ahead). Cheers – Amonet Jan 3 '18 at 21:12
• @KaspervanEck I wish I could share it, but the methods and software I have developed are closely guarded by the client because they are the essence of its business and they view this as a competitive advantage. The time series analysis is just a tiny part of it that I use as a screening tool. There's nothing special or fancy to that; it's coded in R using standard time series packages. – whuber Jan 3 '18 at 23:55

## 1 Answer

Generally speaking, as others have said, the further out your forecast the more likely your prediction errors will increase. With 2 years of data, I would not trust either.

As far as your approach, you're essentially using a seasonal naive approach that averages the past 2 corresponding weeks of the previous seasons.

Assuming you know for a fact this is seasonal data, why not just use seasonal naive? With such limited data, you have no way of knowing if you'll gain or lose accuracy by averaging the last two seasonal periods, so you may as well go with the less complex model (unless, of course, you have some domain knowledge that is swaying you to average them).