May I use the same data in several time series intervals? I am playing with RNNs / LTSMs for a classification task in predicting financial data. 

I have a time-series going many years back, and are planning to divide it into a number of shorter time-intervals that will be used to obtain a classification.

For example divide the data into random length intervals from 30 minutes to 24 hours, with a binary response 'higher' and 'lower' that answers if the value goes higher or lower for the next hours after the interval.

My question is if I can "reuse" the data, as in for example for a certain 24 hour period create the following intervals: 24 hours, 12 hours, 6 hours, 3 hours and 1 hour and train a model on all of these examples. If I do so, obviously the same data will be reused with different responses. 

Or is it better to create a number of models; for example a separate model for 24 hour intervals than the 3 hour intervals?
I dont see a problem in „reusing“ observations. Its just new/different info coming in. The question is more if the model will train/perform well with a short lookback or timelag. Why dont use a long(er) sequence of data to predict (eg) the movement in 3h steps. I wonder why you dont use all the data you have to train the LSTM and update the data stepwise. More data usually is better!