I have multiple data sets (about 15) that describe a process of arriving customers to a shop. When plotted it's pretty clear that over time the rate of customers arriving decreases. However the time axis isn't same in the data sets so one data might be from 2010 to 2014 and one from january 2011 to june 2011. However the shape of the paths are pretty much the same and also the number of arrivals at the end of the data is pretty much same.
I thought that non-homogenous Poisson process might be a good way to model the situation but I'm not sure how to make use of the data properly. I can pretty easily estimate a parameter for a single arrival process (so using only 1 part of the data) but I'm looking for a way to get a better estimation by using all the data. Maybe there is some standard way? All references are very welcome.
So far the methods I have used are: 1) scaling the time axis in all cases to the unit interval 2) making a bucket of parameters to choose from (so individually approximating all the parameters)