(I have asked the same question on math.stackexchange, but I figured that physicists might actually be more likely to have encountered the same problem before.)
I am considering a time series with a fairly cyclical baseline behaviour. By averaging over multiple periods, one might obtain a good prediction for it.
However, there are a bunch of events that occur irregularly. (Even though they usually occur once during each period and are loosely correlated.) Each of these events has a strong and characteristical, but temporally limited impact on my time series.
I am looking for a forecasting method that can handle both the stationary, cyclic background and the spontanous but typical offsets. Does anybody have a suggestion for me?