Forecasting probability distribution of nonlinear time series

Kyongmin Yeo, Igor Melnyk, Nam Nguyen, Eun Kyung Lee

Abstract: 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.

TL;DR: We propose DE-RNN to learn the probability density function of a nonlinear time series by using numerical discretization and to make a forecast of the time evolution of the probability density function by using a sequential Monte Carlo method.

Keywords: Recurrent Neural Network, forecast, density estimation, nonlinear time series, dynamical system, uncertainty quantification