The R Language and Flat Forecasts

About once a week some­one will tell me there is a bug in my fore­cast pack­age for R because it gives fore­casts that are the same for all future hori­zons. To save answer­ing the same ques­tion repeat­edly, here is my response.

A point fore­cast is (usu­ally) the mean of the dis­tri­b­u­tion of a future obser­va­tion in the time series, con­di­tional on the past obser­va­tions of the time series. It is pos­si­ble, even likely in some cir­cum­stances, that the future obser­va­tions will have the same mean and then the fore­cast func­tion is flat.

• A ran­dom walk model will return a flat fore­cast func­tion (equal to the last observed value of the series).
• An ETS(A,N,N) model will return a flat fore­cast function.
• An iid model will return a flat fore­cast func­tion (equal to the mean of the observed data).

This is not a bug. It is telling you some­thing about the time series — namely that there is no trend, no sea­son­al­ity, and insuf­fi­cient tem­po­ral dynam­ics to allow the future obser­va­tions to have dif­fer­ent con­di­tional means.

I dis­cussed this once with another con­sul­tant and he told me that he some­times adds some ran­dom noise to his fore­casts, just to stop his clients ques­tion­ing the flat fore­cast func­tions. Unfor­tu­nately, that increases the fore­cast error, but he thought it was bet­ter to give them what they wanted rather than what was best!