Abstract: We investigate time-dependent data analysis from the perspective of recurrent kernel machines, from which models with hidden units and gated memory cells arise naturally. By considering dynamic gating of the memory cell, a model closely related to the long short-term memory (LSTM) recurrent neural network is derived. Extending this setup to $n$-gram filters, the convolutional neural network (CNN), Gated CNN, and recurrent additive network (RAN) are also recovered as special cases. Our analysis provides a new perspective on the LSTM, while also extending it to $n$-gram convolutional filters. Experiments are performed on natural language processing tasks and on analysis of local field potentials (neuroscience). We demonstrate that the variants we derive from kernels perform on par or even better than traditional neural methods. For the neuroscience application, the new models demonstrate significant improvements relative to the prior state of the art.