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My question is which machine learning techniques can be used to make predictions based on time series data.

My data is of the form of a series of discrete, binary measurements $y_t \in \{0,1\}$ for $t = 1,...,T$ (in my case $T=88$) for a data setof size $n$ (in my case $n \approx 8000$). In addition I have some covariates $X$ containing $p$ features for each sample (in my case $p=40$). The objective is to predict $y_t$.

My data are "participation" data, let's say in a club, where 1 means a participant shows up. So it is possible that there are patterns in the data, e.g. people always showing up, some showing up less and less over time, and others stop showing up altogher.

Preliminary analysis shows that the association between the $y_t$ is much stronger than between $y_t$ and features $X$. Therefore $y_t$ should be used in prediction. In practice, it should be possible to build models for $y_{T+k}$ at time $T$.

I believe a simple AR1 model falls too short. I want to use the full potential of machine learning to solve this prediction problem given the rich time series. Which appoaches should I consider?

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