I am modelling on an univariate time series in a form as shown. Suppose the time interval in the series is daily base, namely every y was collected every day.
I wanna use sliding window method to model this but a key point is that my task is to predict a future y in a 120-day time window, i.e. given all historical data by the time lag t, the model needs to predict y(t+120).
In my understanding, the sliding window methods should be in a way: in the training set, use y(i) as input and y(i+1) as output, iteratively constructed the sample in this way to form the training set, then train the model to predict one step ahead (or multi-steps).
But in my case, I just cared about the status of y after 120 days. But I don't feel confident to predict y(n+120) from y(n) and go n steps ahead. It would be out of control to some extent.
So I planned to construct the training set in a way that: input y(1) output y(121), input y(2) output y(122), ... and so on, then once the model was trained, I could input the latest y status say y(n) and expect the model output y(n+120).
Could someone please advice if my method make sense or how can I revise my methodology to continue my modelling. Highly appreciated.