I'm dealing with about 4,000 stationary time series, most of which I was able to reasonably fit to a distribution based on the KS test. About 200 of the time series, however, were not so well-behaved and frequently consisted of the same value, repeated, and a few noticeable deviations from it.
For example: (200, 200, 200, 200, 200, 10, 200, 200, 200, 180, 200, 200, 200)
The numbers above are fictional but express the point (the data I'm using is proprietary and cannot be shared publicly). My question is: How do you model a process like that? I've been considering maybe some sort of switching mechanism, but with such few observations (each time series has about 50 observations, of which ~45 or more are repeated), any fit seems questionable at best. I also know the data are fundamentally sound after having spoken with the team that produces it -- so dropping these apparent "outliers" does not seem a viable option.
Please help! I've been struggling with this all weekend and am grasping at straws at this point!