I am analyzing a time series (hospital admittance) registered by date - time at hourly frequency, collected all days during 2010 - 2014 (5 years). The time series exhibits seasonality at multiple level (hour, weekday, month). The conditional distribution could be reasonably modeled using a count distribution (Poisson, NegBin). I wonder what could be the best approach for modeling this. I was thinking about a Poisson loglinear model, say $$E\left[admittance_t\right]= \alpha * hour * weekday * month,$$ but I do not know how to account for autocorrelation. I s there an approach to perform this in R? Are there possible alternatives in R?
Collect your data into hourly time buckets and build 24 hourly models and a daily model . Allow top-down and bottom up reconcilliation. Make sure that your daily model includes daily/weekly/monthly/holiday/long-weekend effects etc along with appropriate level shifts/time trends and possible changes in daily patterns along with specific days-of-the-month effects. For example a daily model might encompass and possibly specific weeks within a month or weeks within a quarter and effects like a Monday after a Friday holiday or a Friday before a Monday holiday. If you post your data with some info regarding country source and start date,I will try to be more explicit.