I have found recurrent NNs and their variants (LSTMs and GRUs) to be very useful for the time series I've been working with. It can also be useful to use 1-d convolutional NNs as well. Depending on your data, sometimes working in frequency space can be easier (i.e., train on the FFT of your data). I'm still a neophyte in this area (my background is in astronomy), so I'm learning, too!