I am looking at applying a theoretical best calculation method to some particular time series (ts) data. Ideally the calculation method would encompass relative change in individual ts, volatility of individual ts, individual observation window lengths and individual decay time constants. There would also be two different type of seasons i) weekly and ii) 3 different monthly lengths (e.g. 1 month, 3 months, 8 months). Would ARIMA with harmonic regression for seasonality tick these boxes? Or is there a better theoretical calculation method e.g. ETS?
Thanks in advance!