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!

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  • bug­gy­fun­bunny

    There’s an olde wive’s tale (or may be old crony’s) about the con­sul­tant and the client, to wit…

    client: Mr. Con­sul­tant, please tell me the time! I don’t know what time it is!
    con­sul­tant: Client, give me your hand, there there, all will be well. [client prof­fers left hand, con­sul­tant pushes back sleeve, reveal­ing watch.] Client, it is 10:07 AM
    client: Ah!!! Thank you so much. I was so wor­ried I knew not the time.

  • eric­strom

    Rob, would a com­pro­mise be pos­si­ble ? Fore­cast func­tion pro­vides a note as to why the flat fore­cast (e.g. note the flat fore­cast due to ran­dom walk model being most appropriate).

    By the way, great book and great pack­ages. Thanks much !

  • dan_​

    Rob, this is an excel­lent state­ment. In addi­tion it is so clear and so to the point, sim­ply. Thank you for post­ing it.

  • dp_​planner

    I have just come across this arti­cle. I pro­vide fore­casts to clients for inven­tory opti­miza­tion. When it comes to client, you have to sell the fore­cast. The two main points of sell is cred­i­bil­ity and accu­racy. For a long term out look (more than 2–3 months out), a flat fore­cast is not cred­i­ble since it is there has to be some type of vari­a­tion in the busi­ness going for­ward. Hav­ing said that, a flat fore­cast for a cur­rent month fore­cast, is the most cred­i­ble (from the clients per­spec­tive). That’s the con­stant bat­tle with the client.