Question

I tried using the forecast package in R. When plotting the forecast for a number of samples in the future, I get a constant function. What is the reason of that?

Answer 1

It is a FAQ and so much so that Rob Hyndman (who is the author of the forecast package) felt compelled to write an entire blog post about it: flat forecasts. Allow me to cite:

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.