I have 15-minutely data (96 values per day) over several years for around 340 entities (i.e. 340 data sets or long ts).
Now my task is to forecast a 4-hour window (i.e. 16 observations) for each day in the test set (the last 30% of each entity), for which I use ARIMA models.
In my opinion, it does not make sense to take the whole ts for each entity into account for forecasting the 4-hour window. Because of that, my approach is to take a much shorter period on which I create the Model, for example the last week before the 4-hour window (i.e. 96*7 = 672 Last values).
auto.arima in R takes around 2 minutes to estimate the parameters of the model, I want to estimate the parameters for each entity globally, Meaning: If I have a very long time series (e.g. 105216 data points for an entity), which is stationary and seasonal with a frequency of 96, how would be the approach to determine the Parameters for an ARIMA models which fits best to each 672-data-point-sub-ts (or, more intuitive, each week)?
my initial idea was to loop through each week of the test data, create one model for each week, store the results and compare them for each entity. however, as stated above this takes a lot of time. Is there a better approach?