I'm dealing with a system which monitors and records a time series (half hourly) which I plan to use to build a double seasonal time model (if possible using something that already exists, such as tbats from R's forecast).
My issues is related to the fact that I don't plan to build this model very often. Let's say I have three weeks of data which allowed me to take into account both the daily and weekly seasonalities. Two months later, it's a Tuesday, it's 10AM and I want to make a forecast for 12AM. Do I need to use all the data from the moment I made the model to this current date, or is there a way I can use a shorter period (such as the current day data) ? Speed is paramount and if I need to make a forecast every half an hour, I would really like only using a reduced period of time to make the forecast.
I'm basically looking for a method for dealing with growing time series as most literature deals with a static data sets.