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I got a very long sequence of binary items (0 or 1). Each item is associated to a timestamp. For example :

Monday, 03:00 AM, 17th January 2010, 0
Monday, 04:00 AM, 17th January 2010, 0
Monday, 05:00 AM, 17th January 2010, 1
Monday, 06:00 AM, 17th January 2010, 1
Monday, 07:00 AM, 17th January 2010, 0
Monday, 08:00 AM, 17th January 2010, 1
...

I got a strong assumption that 0s and 1s depend on static features like the day of the week (or the hour of the day) BUT also might depend on the recent history. I'm looking for a model that would be able to predict the very next item knowing all the previous ones. What would you suggest me? I'm ok with everything even deep learning.

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You should look into LSTM or Hidden Markov models that are able to capture the time series evolution of the pattern in your data.

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