I am no expert in deep learning, I do not want to get you in the wrong direction. But to my knowledge, you can at least try a harmonic regression approach, which I found to be very effective in a dataset similar to yours. You can check the following link: otexts.com/fpp2/dhr.html I also suggest you add another plot of your dataset showing your series in long run so that others can provide a better answer by investigating possible patterns.

it seems that your data is highly periodic. have you considered classical approaches before going into lstm?

@Stef take (Y|X=x) as a whole. This implies that the conditional distribution of Y given an observed value of X=x follows a Bernoulli distribution, which is parametrized as a function of x.

I think you should first test for autocorrelation in both categories, because observed data measured over time do not necessarily need to be treated as time series. That is, next values may be unrelated to the previous ones. If you can treat each category as iid samples you can do distribution fitting. Not posting this as an answer because it is not thorough enough.

i doubt this series in non-stationary, i think if you remove the trend (which i believe is sinusoidal) the mean and variance remains relatively same

could you post the graph of your series without the arima estimation? it is hard to see the exact pattern here

@whuber that's one of the reasons why i figured including mean as well would probably be a better way to go, but i guess experimenting with different ideas is necessary in such a problem. What do you suggest?