Iclr 2018 F Orecasting P Robability D Istribution of N on - Linear T Ime S Eries

We propose DE-RNN to learn the probability density function (PDF) of a nonlinear time series, and compute the temporal evolution of the PDF for a probabilistic forecast. A Recurrent Neural Network (RNN) based model is employed to learn a nonlinear operator for temporal evolution of the stochastic process. We use a softmax layer for a numerical discretization of a PDF, which transforms a function approximation problem to a classification problem. Explicit and implicit regularization strategies are introduced to impose a smoothness condition on the estimated probability distribution. A multiple-step forecast is achieved by computing the time evolution of PDF.