Multivariate time series classification
Following up on the comment about deep learning, with high dimensional time series data you would be much better served with a recurrent-type of deep model. For example, an LSTM is a very good starting point with high-dimensional data. This may be a good place to start: Sequence Classification with LSTM Recurrent Neural Networks in Python with Keras 

Although CNNs are very useful for high-dimensional data, when you have a time series, it's best to start with a model that is designed for a time series. A CNN may do well, and you should compare your results to a CNN, but it is not a time series model.