Background:

There is an aggregated measure represented by a variable A, modeled as a time series from a process. There was a need forecast A and also to find out the historical amount of data of A that is the best reflector of future values of A (as there was a data storage capacity issue). Using a combination of sliding window regression technique and ARIMA, it is found that the size of the sliding window out of different window sizes tried, is 100 (as it gave lesser MAPE than the rest of the ones). So the past 100 values of A is a better reflector of future. This forecast was successful.

“A” aggregation comes from B and C of the same process, such that A=B+C and there is a need to predict these variables as a percentage of A. B and C are modeled as a time series.

Questions:

Can the same window size (100 as determined in the previous step) be used to predict B and C as a percentage of A using ARIMA?

Since B and C are expressed as a percentage of A, is it ok to predict B and then calculate C as (100-B) as time series B and C will be mirrored, meaning the same ARIMA parameters will hold good?

Any thoughts and recommendations?

Note: Forecasting B and C and then calculating A may be a good option, but following a deductive approach is important here