Do we need to tune same model differently for different window sizes in time series data classification? I am currently working on the time series data classification problem using deep learning. As we all know that in time series, we process the time-series data sequentially for some time steps at a time through the model which is called as a window. We slide the window and the next window is our input again. Since I have just started working in deep learning and time-series domain, my question is if we tune some deep learning model for some window size , let's say 10 then should the same tuned model be used to get the near accuracies for some different window(say 15) on the same data or the model should be tuned again for the latter window. 

Currently,if I am using the same model for a different window then I get the accuracy decreased by 4-5% from the previous window. From this I believe that window size again is a hyperparameter which when changed requires the model to be tuned again. 

So, what is the right thing in this case? Should the same model be used or should it be tuned again? I tried searching this online but I couldn't get any help on this. Help is appreciated as I am new to this domain.
In my opinion it should be tuned again.
Reasoning:
Using different window size is almost equivalent to using different features(as in a non time-series modeling). Tuning hyper-parameters is usually done after features were selected(I.E for a given set of features).