Model approach for count data with a large range of y values I am modeling ridership data for specific routes by month over a number of years.  Some routes have as little as about 1000 riders per month while other routes may have over 20,000 riders per month.  I have been looking at different approaches to model this data including a panel data model and a generalized linear data model (poisson family).  However, I have found some information that says you should only use the poisson family when you have a small range in data for the y variable.  
Is there a better approach to modeling count data with a large range of y values than Poisson?  
 A: For count data it is indicated (for reasons of interpretability of estimated parameters) to use a generalized linear model (GLM) with logarithmic link function, see my answer to Goodness of fit and which model to choose linear regression or Poisson
But the distribution family can be choosen in different ways. The reason for the advice you refer, to use Poisson regression when the counts are not to large, is that usually with large counts there is overdispersion, that is, the variance is larger than the variance of the Poisson. 
That can be solved in various ways, like using (in R terminology) a quasipoisson family, which can be good enough. Or you can use a negative binomial family. Or, especially if you only wants predictions from the model and not need interpretable parameters, use the traditional way of a usual linear model (that is, identity link function) for the response $\sqrt{Y}$. The square-root transformation is (approximately) variance stabilizing for the Poisson (and quasi-Poisson) families. Look at Why is the square root transformation recommended for count data?   for an explanation of this!
For more about overdispersion, see  Modelling a Poisson distribution with overdispersion    and    Comparing  overdispersion distributions
A: I am a little bit confused by the question (and the answer) as Box and Jenkins introduced ARIMA modelling by analyzing count data i.e. the number of people that flew in a particular month with their airline series. If the time series has small count numbers e.g. 0.0,1,1,0,1,0,2,1,0,0,1,2,1,2,0,1,..... there are definite problems/limitations applying ARIMA modelling procedures. I have been reasonably happy with count data that can average 5 or more as the assumption of continuity is less strained. Truncating/rounding the forecast is a way of providing an answer that must be an integer as integers only exist in the history.
