Multivariate time series classification I have around 72,000 Multivariate time series (MTS) with four Dimensions and of Length around 3000 milliseconds(not constant). It is (4*3000*72000) DLN. This MTS has tow possible outcomes either Pass or Fail.

How to select a better classifier that suits above criteria?

I have read some implementations of MTS classification. I cannot apply distance measure techniques for classification as the data is too lengthy and is not constant when compare to other MTS. 

I am considering to apply below techniques for classification 

1) Extract global statistical features from data and apply any classifier(KNN or Random Forest or neural networks)

what would be the best approach. Please guide me better technique and I am also open for other techniques to classify MTS
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.